Non-abelian cohomology of Lie H-pseudoalgebras and inducibility of automorphisms

2023/12/16 by Apurba Das, Das, Apurba
Biochemistry, Genetics and Molecular Biology · Mathematics · #16S70 #17B40 #17B55 #17B56 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Sphingolipid Metabolism and Signaling

paper · pdf · doi:10.48550/arxiv.2312.10341

openalex publication_date 2023/12/16 · openalex created_date 2023/12/20 · openalex updated_date 2026/07/28

Abstract

The notion of Lie H-pseudoalgebra is a higher-dimensional analogue of Lie conformal algebras. In this paper, we classify the equivalence classes of non-abelian extensions of a Lie H-pseudoalgebra L by another Lie H-pseudoalgebra M in terms of the non-abelian cohomology group H²_nab (L, M). We also show that the group H²_nab (L, M) can be realized as the Deligne groupoid of a suitable differential graded Lie algebra. Finally, we consider the inducibility of a pair of Lie H-pseudoalgebra automorphisms in a given non-abelian extension. We show that the corresponding obstruction can be realized as the image of a suitable Wells map in the context.

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