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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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Multipliers, covers, and stem extensions for Lie superalgebras
Suppose that the underlying field is of characteristic different from 2 and 3. We first prove that the so-called stem deformations of a free...
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Cohomology and Deformations of 3-Dimensional Heisenberg Hom-Lie Superalgebras
We study Hom-Lie superalgebras of Heisenberg type. For 3-dimensional Heisenberg Hom-Lie superalgebras we describe their Hom-Lie super structures,...
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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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On the Cohomology of Lie Algebras with an Invariant Inner Product
In this work we consider the moduli space of all noncommutative metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over
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Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras
We introduce the notion of quasi-trace functions on Lie algebras. As applications we study realizations of 3-dimensional and 4-dimensional 3-Lie...
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Formal Deformations and Principal Series Representations of SL(2, ℝ) and SL(2, ℂ)
In this note, we study formal deformations of derived representations of the principal series representations of SL(2, ℝ). In particular, we recover...
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Deformations on the Twisted Heisenberg-Virasoro Algebra
With the cohomology results on the Virasoro algebra, the authors determine the second cohomology group on the twisted Heisenberg-Virasoro algebra,...
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Deformations and generalized derivations of Hom-Lie conformal algebras
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal...
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A New Approach to Representations of 3-Lie Algebras and Abelian Extensions
In this paper, we introduce the notion of generalized representation of a 3-Lie algebra, by which we obtain a generalized semidirect product 3-Lie...
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1-Cocycles on the group of contactomorphisms on the supercircle S 1|3 generalizing the Schwarzian derivative
The relative cohomology H diff 1 (K(1|3), osp(2, 3); D γ,µ ( S 1|3 )) of the contact Lie superalgebra K(1|3) with coefficients in the space of differential...
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A cohomological obstruction to the existence of compact Clifford–Klein forms
In this paper, we continue the study of the existence problem of compact Clifford–Klein forms from a cohomological point of view, which was initiated...
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N-point Virasoro Algebras Considered as Krichever–Novikov Type Algebras
We explain how the recently again discussed N-point Witt, Virasoro, and affine Lie algebras are genus zero examples of the multi-point versions of...
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Derived Varieties of Complexes and Kostant’s Theorem for \(\mathfrak{gl}(\mathrm{m}|\mathrm{n})\)
Given a graded vector space V, the variety of complexes Com(V) consists of all differentials making V into a cochain complex. This variety was first...
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On the deformation of Lie-Yamaguti algebras
The deformation theory of Lie-Yamaguti algebras is developed by choosing a suitable cohomology. The relationship between the deformation and the...
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Lie Superalgebras of Krichever–Novikov Type
Classically, starting from the Witt and Virasoro algebra important examples of Lie superalgebras were constructed. In this write-up of a talk...
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Cohomology of the Schrödinger algebra S(1)
We explicitly compute the first and second cohomology groups of the Schrödinger algebra S (1) with coefficients in the trivial module and the...