Search

The concept of -differential operators is a natural generalization of differential operators and difference operators. In this paper, we determine the -differential Lie algebraic structure on the Witt algebra and the Virasoro algebra for invertible. Then we consider several families of modules over the Virasoro algebra with explicit module actions and determine the -differential module structures on them. [ABSTRACT FROM AUTHOR]

The super-Virasoro algebras, also known as the superconformal algebras, are nontrivial graded extensions of the Virasoro algebra to Lie superalgebra version. In this paper, we classify the compatible left-symmetric superalgebra structures on the N = 2 Ramond and Neveu-Schwarz superconformal algebras under certain conditions, which generalizes the corresponding results for the Witt, Virasoro and super Virasoro algebras. [ABSTRACT FROM AUTHOR]

In this paper, we determine the biderivations of the block Lie algebras B ( q ) for all q ∈ C . More precisely, we prove that the space of biderivations of B ( q ) is spanned by inner biderivations and one outer biderivation. Applying this result we also find all commuting maps on B ( q ) . [ABSTRACT FROM AUTHOR]

We construct a class of modules over the affine Lie algebra sl ˆ 2 from the modules over the degree-2 Weyl algebra K 2 and modules over the 2-dimensional solvable Lie algebra b. We determine the irreducibility and isomorphisms of these modules with examples given by Bavula's construction of modules for generalized Weyl algebras in [5]. Finally, we show these irreducible sl ˆ 2 -modules are generally new. [ABSTRACT FROM AUTHOR]

In Tang and Bai [Math Nachr. 2012;285:922–935] classified a class of non-graded left-symmetric algebraic structures on the Witt algebra under a certain rational condition. In this note, we show that this rational condition is not necessary. This leads to a more elegant classification of the left-symmetric algebraic structures and Novikov algebraic structures on the Witt algebra. [ABSTRACT FROM AUTHOR]

In this paper, we study Whittaker modules over Virasoro-like algebra relative to some total order. We determine all Whittaker vectors and the irreducibilities of the universal Whittaker modules. For the reducible ones, we determine their unique maximal submodules, and the corresponding irreducible quotient modules are just those modules constructed by Batra et al. [J. Algebra 322(12), 4163-4180 (2009)]. Using their results we can deduce more properties on the maximal submodules and irreducible modules. [ABSTRACT FROM AUTHOR]

In this article, we study Whittaker modules over generalized Virasoro algebras relative to some total order. We give the description of any Whittaker module and its Whittaker vectors. In particular, we determine all simple Whittaker modules, which provide the first known examples of simple nonweight modules over generalized Virasoro algebras. On the other hand, we also show that any Whittaker module over any generalized Virasoro algebra can be induced from a Whittaker module over some Virasoro subalgebra. [ABSTRACT FROM PUBLISHER]

In this paper, we study a class of Z d -graded modules, which are constructed using Shen–Larsson's functor from sl d -modules V , for the Lie algebras of divergence zero vector fields on tori and quantum tori. We determine the irreducibility of these modules for finite-dimensional or infinite-dimensional V using a unified method. In particular, these modules provide new irreducible weight modules with infinite-dimensional weight spaces for the corresponding algebras. [ABSTRACT FROM AUTHOR]