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Symmetric (co)homologies of Lie algebras

✍ Scribed by A.S. Dzhumadil’daev

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
317 KB
Volume
324
Category
Article
ISSN
0764-4442

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✦ Synopsis

Cohomologies of Lie algebras are usually calculated using the Chevalley-Eilenberg cochain complex of skew-symmetric forms . We consider two cochain complexes consisting of forms with some symmetric propert ies. First. cocha ins C' (L) are symmetric in the last 2 argument s, skew-symmetric in the others and satify moreover some kind of Jacobi condition in the last 3 argument s. In characteristic 0, its cohomologies are isomorphic to the cohomologies of the factor-complex C• (L, L') jC• + I (L , K ). Second, a symmetric version C~( A ) is defined for an assoc iative algebra A. It is a subcomplex of the cyclic cochain complex . These symmetric cochain complexes are used for the calculation of 3-cohomoJogies of Cartan Type Lie algebras with trivial coefficients. 0764

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