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Maurer-Cartan characterizations and cohomologies of compatible Lie algebras
In this paper, we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie algebras. Explicitly, we first introduce the...
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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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Characters for extended affine Lie algebras: a combinatorial approach
The behavior of objects associated with general extended affine Lie algebras is typically distinct from their counterparts in affine Lie algebras....
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Deformed Cartan matrices and generalized preprojective algebras II: general type
We propose a definition of deformed symmetrizable generalized Cartan matrices with several deformation parameters, which admit a categorical...
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Wild Local Structures of Automorphic Lie Algebras
We study automorphic Lie algebras using a family of evaluation maps parametrised by the representations of the associative algebra of functions. This...
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Local and 2-Local Derivations of Locally Simple Lie Algebras
In the present paper we study local and 2-local derivations of the classical locally simple Lie algebras. Firstly, we prove that every local and...
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On the Semisimple Orbits of Restricted Cartan Type Lie Algebras W, S and H
In this short note, we give a description of semisimple orbits in the restricted Cartan type Lie algebras W , S , H .
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Finite Dimensional Lie Algebras
Another fertile field to explore the link between algebraic relations of the matrices and the properties of their characteristic polynomial is where...
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Character Sheaves for Classical Graded Lie Algebras
In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type II...
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On Some Classes of Bases in Finite-Dimensional Lie Algebras
AbstractIn the paper, Lie algebras having bases of a special form (nice and beautiful bases) are considered. For nice bases, it is proved that, in...
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Real non-degenerate two-step nilpotent Lie algebras of dimension eight
We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex...
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Local Derivations of Classical Simple Lie Algebras
The paper is devoted to study of local derivations on classical simple Lie algebras. We prove that every local derivation on an arbitrary classical...
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Commuting Toeplitz Operators and Moment Maps on Cartan Domains of Type III
Let \(D^{III}_n\) and...
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Fundamentals of the Theory of Lie Algebras and Root Systems
In order to develop the theory of zeta-functions of root systems, it is surely necessary to understand the theory of Lie algebras and root systems....
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New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories
Using tensor categories, we present new constructions of several of the exceptional simple Lie superalgebras with integer Cartan matrix in...
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Inner Ideals of Real Simple Lie Algebras
A classification up to automorphism of the inner ideals of the real finite-dimensional simple Lie algebras is given, jointly with precise...
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SYMPLECTIC DIRAC OPERATORS FOR LIE ALGEBRAS AND GRADED HECKE ALGEBRAS
The aim of this paper is to define a pair of symplectic Dirac operators ( D + , D – ) in an algebraic setting motivated by the analogy with the algebraic...