CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras. | Zendy

Jean-Louis Loday | Zendy

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CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.

Author(s) -

Jean-Louis Loday

Publication year - 1995

Publication title -

mathematica scandinavica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.553

H-Index - 30

eISSN - 1903-1807

pISSN - 0025-5521

DOI - 10.7146/math.scand.a-12560

Subject(s) - mathematics , dual (grammatical number) , cohomology , pure mathematics , product (mathematics) , cup product , algebra over a field , equivariant cohomology , de rham cohomology , geometry , linguistics , philosophy

For any Lie algebra g there is a notion of Leibniz cohomology HL(g), which is defined like the classical Lie cohomology, but with the n-th tensor product g⊗n in place of the n-th exterior product Λ g. This Leibniz cohomology is defined on a larger class of algebras : the Leibniz algebras (cf. [L1], [L2]). A Leibniz algebra is a vector space equipped with a product satisfying a variation of the Jacobi identity :

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