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Abstract: Let be a class of unital C*-algebras. The class of C*-algebras which can be tracially approximated (in the Egorov-like sense first considered by Lin) by the C*-algebras in is studied (Lin considered the case that consists of finite-dimensional C*-algebras or the tensor products of such with ). In particular, the question is considered whether, for any simple separable , there is a C*-algebra B which is a simple inductive limit of certain basic homogeneous C*-algebras together with C*-algebras in , such that the Elliott invariant of A is isomorphic to the Elliott invariant of B. An interesting case of this question is answered. In the final part of the paper, the question is also considered which properties of C*-algebras are inherited by tracial approximation. (Results of this kind are obtained which are used in the proof of the main theorem of the paper, and also in the proof of the classification theorem of the second author given in [Z. Niu, A classification of tracially approximately splitting tree algebra, in preparation] and [Z. Niu, A classification of certain tracially approximately subhomogeneous C*-algebras, PhD thesis, University of Toronto, 2005]—which also uses the main result of the present paper.) [Copyright &y& Elsevier]

Abstract: In this paper we complete a distributional Fourier analysis developed by Howell in a serie of papers. We investigate convolution operators in the corresponding distribution spaces. [Copyright &y& Elsevier]

Abstract: In this paper we study the concept of a Cartan subalgebra in the context of locally finite and Borcherds–Kac–Moody Lie algebras. [Copyright &y& Elsevier]

Abstract: Let L be a Lie algebra. We call a linear map a near-derivation if there exists a linear map such that is a derivation for every . The paper is devoted to describing the structure of near-derivations in certain Lie algebras arising from associative ones. [Copyright &y& Elsevier]

Abstract: Hanaki [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195–201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363–369] generalized many properties of characters of finite groups to characters of association schemes. In this paper we show that many of these properties also hold for table algebras. Our approach is not to generalize the proofs in [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195–201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363–369] to table algebras, but to prove many stronger properties, and then obtain results in [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195–201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363–369] as direct consequences. [Copyright &y& Elsevier]

Abstract: In this paper we prove a formula for fusion coefficients of affine Kac–Moody algebras first conjectured by Walton [M.A. Walton, Tensor products and fusion rules, Canad. J. Phys. 72 (1994) 527–536], and rediscovered by Feingold [A. Feingold, Fusion rules for affine Kac–Moody algebras, in: N. Sthanumoorthy, Kailash Misra (Eds.), Kac–Moody Lie Algebras and Related Topics, Ramanujan International Symposium on Kac–Moody Algebras and Applications, Jan. 28–31, 2002, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India, in: Contemp. Math., vol. 343, American Mathematical Society, Providence, RI, 2004, pp. 53–96]. It is a reformulation of the Frenkel–Zhu affine fusion rule theorem [I.B. Frenkel, Y. Zhu, Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J. 66 (1992) 123–168], written so that it can be seen as a beautiful generalization of the classical Parthasarathy–Ranga Rao–Varadarajan tensor product theorem [K.R. Parthasarathy, R. Ranga Rao, V.S. Varadarajan, Representations of complex semi-simple Lie groups and Lie algebras, Ann. of Math. (2) 85 (1967) 383–429]. [Copyright &y& Elsevier]

Abstract: This paper compares the expressiveness of different fragments of ambient calculi via leader election problems. We consider Mobile Ambients (MA), Safe Ambients (SA) and the Push and Pull Ambient Calculus (PAC). Cardelli and Gordon encoded the asynchronous π-calculus into MA. Zimmer has shown that the synchronous π-calculus without choice can be encoded in pure (no communication) SA. We show that pure MA without restriction has symmetric electoral systems, that is, it is possible to solve the problem of electing a leader in a symmetric network. By the work of Palamidessi, this implies that this fragment of MA is not encodable (under certain conditions) in the π-calculus with separate choice. Moreover, we use the same technique to show that fragments of SA and PAC are not encodable (under certain conditions) in the π-calculus with separate choice. We also show that particular fragments of ambient calculi do not admit a solution to leader election problems, in the same way as the π-calculus with separate choice. This yields a fine-grained hierarchy within ambient calculi. [Copyright &y& Elsevier]

Abstract: For any vertex algebra and any subalgebra , there is a new subalgebra of known as the commutant of in . This construction was introduced by Frenkel–Zhu, and is a generalization of an earlier construction due to Kac–Peterson and Goddard–Kent–Olive known as the coset construction. In this paper, we interpret the commutant as a vertex algebra notion of invariant theory. We present an approach to describing commutant algebras in an appropriate category of vertex algebras by reducing the problem to a question in commutative algebra. We give an interesting example of a Howe pair (i.e., a pair of mutual commutants) in the vertex algebra setting. [Copyright &y& Elsevier]

Abstract: In this paper, the notion of generalized umbrella rings is introduced. We show that every generalized umbrella ring is a stably coherent ring. As an application, we show that every finitely generated projective module over is free if R is a generalized umbrella ring with weak global dimension two. [Copyright &y& Elsevier]

Abstract: In this paper, we study the weak convergence of “Leray-type” solutions of a magneto-hydro-dynamic systems. The proofs are based on weak compactness arguments and linear algebra methods. [Copyright &y& Elsevier]

Abstract: Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic . We prove in this paper that if for every torus T of maximal dimension in the p-envelope of adL in DerL the centralizer of T in adL acts triangulably on L, then L is either classical or of Cartan type. As a consequence we obtain that any finite-dimensional simple Lie algebra over an algebraically closed field of characteristic is either classical or of Cartan type. This settles the last remaining case of the generalized Kostrikin–Shafarevich conjecture (the case where ). [Copyright &y& Elsevier]

Abstract: In this paper we prove that a Lie algebra L is strongly prime if and only if for every nonzero elements . As a consequence, we give an elementary proof, without the classification theorem of strongly prime Jordan algebras, of the fact that a linear Jordan algebra or Jordan pair T is strongly prime if and only if for every . Moreover, we prove that the Jordan algebras at nonzero Jordan elements of strongly prime Lie algebras are strongly prime. [Copyright &y& Elsevier]

Abstract: In [J. Du, Q. Fu, J.-P. Wang, Infinitesimal quantum and little q-Schur algebras, J. Algebra 287 (2005) 199–233], little q-Schur algebras were introduced as homomorphic images of infinitesimal quantum in the odd root of unity case. In this paper, we shall introduce little q-Schur algebras at even roots of unity. We shall construct various bases for and give the dimension formula of . [Copyright &y& Elsevier]

Abstract: It is well known that the second homology group of the Steinberg Lie algebra is trivial when . In this paper, we will work out explicitly for which are not necessarily trivial. Consequently, we obtained for . [Copyright &y& Elsevier]

Abstract: In this paper, finite-dimensional solvable Lie algebras with nondegenerate invariant bilinear forms are classified. The classification is based on the investigation of the minimal generating sets, which are proved to be one of the three types: paired type, isolated type and mixed type. [Copyright &y& Elsevier]

Abstract: Let G be a simple simply connected affine algebraic group over an algebraically closed field k of characteristic p for an odd prime p. Let B be a Borel subgroup of G and U be its unipotent radical. In this paper, we determine the second cohomology groups of B and its Frobenius kernels for all simple B-modules. We also consider the standard induced modules obtained by inducing a simple B-module to G and compute all second cohomology groups of the Frobenius kernels of G for these induced modules. Also included is a calculation of the second ordinary Lie algebra cohomology group of Lie(U) with coefficients in k. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with the problem of framing 2-variable 2-parameter Bessel functions (2V2PBF) into the context of the representation of the 3-dimensional Lie algebra . Further, we derive generating relations and identities involving 2V2PBF. Furthermore, we deduce some new and known relations involving various other forms of generalized Bessel functions (GBF) and Bessel functions (BF) as applications of these results. [Copyright &y& Elsevier]

Abstract: In this paper we continue the investigation of Cohen–Macaulay projective monomial curves begun in [Les Reid, Leslie G. Roberts, Non-Cohen–Macaulay projective monomial curves, J. Algebra 291 (2005) 171–186]. In the process we introduce maximal curves. Cohen–Macaulay curves are maximal, but not conversely. We show that the number of all curves of degree d that are Cohen–Macaulay grows exponentially, but not as fast as the total number of curves, and also that maximal curves of degree d with sufficiently large embedding dimension relative to d are Cohen–Macaulay. [Copyright &y& Elsevier]

Abstract: Let k be an algebraically closed field and A be a tree algebra. We consider here a class obtained by the blowing-up of a tree algebra A at a set of vertices D of A, such an algebra is denoted by . The objective of this paper is to prove the equivalence between the derived-tameness and the non-negativity of the Euler form for algebras of this form. We also show that, in this case, if D is a non-empty set then must be derived equivalent to a special incidence algebra, called semichain algebra. [Copyright &y& Elsevier]

Abstract: The main aim of this paper is to better understand the localization technique for certain Noetherian rings like enveloping algebras of nilpotent Lie algebras. For such rings R we also give a conjectural definition of certain sheaves which should be “affine” objects naturally generalizing the classically defined structure sheaves in commutative theory. The corresponding sheaves associated to some R-modules might carry particularly interesting information; e.g., for representation theory of semisimple Lie groups. Next, we generalize one important theorem of P.F. Smith on localization in Noetherian Artin–Rees rings. As an interesting corollary we obtain that every prime ideal of height 1 in the enveloping algebra of the Lie algebra over a field of characteristic zero is localizable. Finally, we provide a number of concrete useful calculations for our main example, the enveloping algebra of the three-dimensional Heisenberg Lie algebra; and thus test both the proposed ideas and methods. In particular, we introduce the notion of a weakly normal element, generalizing the notion of a normal element. [Copyright &y& Elsevier]

Abstract: In this paper we introduce the notion of Jordan socle for nondegenerate Lie algebras, which extends the definition of socle given in [A. Fernández López et al., 3-Graded Lie algebras with Jordan finiteness conditions, Comm. Algebra, in press] for 3-graded Lie algebras. Any nondegenerate Lie algebra with essential Jordan socle is an essential subdirect product of strongly prime ones having nonzero Jordan socle. These last algebras are described, up to exceptional cases, in terms of simple Lie algebras of finite rank operators and their algebras of derivations. When working with Lie algebras which are infinite dimensional over an algebraically closed field of characteristic 0, the exceptions disappear and the algebras of derivations are computed. [Copyright &y& Elsevier]

Abstract: The groups in this paper are abelian. In this Addendum to [T.G. Faticoni, The class number of an abelian group, J. Algebra 314 (2007) 978–1008] we show that a problem in the direct sum decompositions of torsion-free finite rank groups implies several important problems of number theory. [Copyright &y& Elsevier]