Derivations and crossed modules of 3-Lie-Rinehart algebras

doi:10.3969/j.issn.1000-1565.2021.02.001

Abstract

Abstract: For a given commutative associative algebra A, and a 3-Lie algebra L and a 3-Lie A -algebra R over a field F of characteristic zero, derivations from the 3-Lie-Rinehart algebra(L,A,ρ)to the 3-Lie A -algebra(R,A), and crossed modules(R,A,β,∂)of 3-Lie-Rinehart algebras are studied. Derivations from 3-Lie-Rinehart algebras to 3-Lie A-algebras are characterized by means of 3-Lie-Rinehart algebra homomorphisms.

Key words: 3-Lie algebra, 3-Lie-Rinehart algebra, derivation, crossed module

CLC Number:

O152.5

BAI Ruipu, LI Xiaojuan. Derivations and crossed modules of 3-Lie-Rinehart algebras[J]. Journal of Hebei University(Natural Science Edition), 2021, 41(2): 113-118.

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