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Given two epimorphisms of algebrasA ↠ BandC ↠ B, we consider the pullbackR. We introduce a particular class of algebras, thetree oriented pullback, where there is a close relationship between the category of indecomposable modules of these algebras. This leads us to prove that ifAandCare hereditary algebras, thenRis a tilted algebra. [ABSTRACT FROM AUTHOR]

Abstract: We study -graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac–Moody Lie algebras. We construct new families of such irreducible modules over Heisenberg Lie algebras. Our main result establishes the irreducibility of the corresponding generalized loop modules providing an explicit construction of many new examples of irreducible modules for affine Lie algebras. In particular, to any function we associate a φ-highest weight module over the Heisenberg Lie algebra and a φ-imaginary Verma module over the affine Lie algebra. We show that any φ-imaginary Verma module of nonzero level is irreducible. [Copyright &y& Elsevier]

Abstract: We determine derived representation type of complete finitely generated local and two-point algebras over an algebraically closed field. [Copyright &y& Elsevier]