Universal Central Extensions of Leibniz Superalgebras Over Superdialgebras
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DOI: 10.1007/s00009-017-0842-9
Abstract: We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of $$\mathfrak {sl}(m, n, D)$$sl(m,n,D) when $$m+n \ge 3$$m+n≥3 and D is a superdialgebra, solving, in particular, the problem… read more here.
Keywords: leibniz superalgebras; superalgebras superdialgebras; central extensions; universal central ... See more keywords
Finite presentability of universal central extensions of sln(R)
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DOI: 10.1016/j.jalgebra.2020.09.016
Abstract: Abstract In this paper we discuss finite presentability of the universal central extensions of Lie algebras sl n ( R ) , where n ≥ 3 and R is a unital associative k-algebra. We show… read more here.
Keywords: universal central; central extensions; presentability universal; extensions sln ... See more keywords
Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
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DOI: 10.1016/j.jpaa.2017.08.017
Abstract: Abstract We describe the space of central extensions of the associative algebra Ψ n of formal pseudo-differential symbols in n ≥ 1 independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology… read more here.
Keywords: central extensions; formal pseudo; pseudo differential; hochschild homology ... See more keywords
Universal central extensions of current Lie superalgebras
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DOI: 10.1016/j.jpaa.2019.106205
Abstract: Abstract We identify the universal central extension of g = A ⊗ k , where k is a finite dimensional perfect Lie superalgebra equipped with a nondegenerate homogeneous invariant supersymmetric bilinear form κ which is… read more here.
Keywords: lie superalgebras; universal central; central extensions; lie ... See more keywords
Restricted one-dimensional central extensions of restricted simple Lie algebras
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DOI: 10.1016/j.laa.2016.09.037
Abstract: Abstract We study the restricted one-dimensional central extensions of an arbitrary finite dimensional restricted simple Lie algebra for p ≥ 5 . For H 2 ( g ) = 0 , we explicitly describe the… read more here.
Keywords: central extensions; restricted simple; one dimensional; simple lie ... See more keywords
Isoclinic extensions of Lie superalgebras
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DOI: 10.1080/00927872.2020.1836188
Abstract: Abstract We study the notion of isoclinism on central extensions of Lie superalgebras and discuss some conditions under which central extensions are isoclinic as well as some results on isoclinic homomorphisms of central extensions. We… read more here.
Keywords: isoclinic extensions; lie superalgebras; extensions lie; central extensions ... See more keywords
A note on the representation theory of central extensions of reductive p-adic groups
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DOI: 10.1080/00927872.2023.2209647
Abstract: In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups. read more here.
Keywords: note representation; reductive adic; central extensions; representation theory ... See more keywords