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Finite Dimensional Modules over Indefinite Kac–Moody Lie Algebras
In this paper, we study the finite dimensional modules over indefinite Kac–Moody Lie algebras. We prove that any Kac–Moody Lie algebra with...
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Whittaker Modules over the N = 2 Super-BMS3 Algebra
This paper focuses on the analysis of Whittaker modules and high-order Whittaker modules over the N = 2 super-BMS 3 algebra. We provide a...
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Hom-Lie Algebras with Derivations
In this paper, we first introduce the notion of an HLieDer triple, which includes a Hom-Lie algebra and a derivation. We define a cohomology theory...
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Conformal biderivations of loop W(a, b) Lie conformal algebra
We study conformal biderivations of a Lie conformal algebra. First, we give the definition of a conformal biderivation. Next, we determine the...
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Super Kupershmidt Operators on Pre-malcev Superalgebras
The main purpose of this paper is to study a generalization of pre-Malcev algebras and pre-Lie superalgebras, which is called pre-Malcev...
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Imaginary Modules over the Affine Nappi—Witten Algebra
In this paper, we consider the imaginary highest weight modules and the imaginary Whittaker modules for the affine Nappi—Witten algebra. We show that...
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Singular Conformal Oscillator Representations of Orthosymplectic Lie Superalgebras
In our earlier paper, we generalize the one-parameter ( c ) family of inhomogeneous first-order differential operator representations of the orthogonal...
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On finite-dimensional representations of finite W-superalgebras
We first formulate and prove a version of Premet’s conjecture for finite W -superalgebras associated with basic Lie superalgebras. As in the case of W -...
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External Vertices for Crystals of Affine Type A
We demonstrate that for a fixed dominant integral weight and fixed defect d , there are only a finite number of Morita equivalence classes of blocks...
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On Chevalley Restriction Theorem for Semi-reductive Algebraic Groups and Its Applications
An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical. Such a semi-reductive...
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A Generalization of the Correspondences Between Quasi-Hereditary Algebras and Directed Bocses
Quasi-hereditary algebras were introduced by Cline, Parshall and Scott to study the highest weight categories in Lie theory. On the other hand,...
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Gröbner Bases for Fusion Products
We provide a new approach towards the analysis of the fusion products defined by B. Feigin and S. Loktev in the representation theory of (truncated)...
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Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras
This paper extends the well-known fact that a Rota-Baxter operator of weight 0 on a Lie algebra induces a pre-Lie algebra, to the level of...