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- W1499350750 abstract "For a Lie-Rinehart algebra (A,L), generators for the Gerstenhaber algebra Lambda_A L correspond bijectively to right (A,L)-connections on A in such a way that B-V structures correspond to right (A,L)-module structures on A. When L is projective as an A-module, given an exact generator partial, the homology of the B-V algebra (Lambda_A L,partial) coincides with that of L with coefficients in A with respect to the right (A,L)-module structure determined by partial. When L is also of finite rank n, there are bijective correspondences between (A,L)-connections on Lambda_A^nL and right (A,L)-connections on A and between left (A,L)- module structures on Lambda_A^nL and right (A,L)-module structures on A. Hence there are bijective correspondences between (A,L)-connections on Lambda_A^n L and generators for the Gerstenhaber bracket on Lambda_A L and between (A,L)-module structures on Lambda_A^n L and B-V algebra structures on Lambda_A L. The homology of such a B-V algebra (Lambda_A L,partial) coincides with the cohomology of L with coefficients in Lambda_A^n L, for the left (A,L)-module structure determined by partial. Some applications are discussed." @default.
- W1499350750 created "2016-06-24" @default.
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- W1499350750 date "1997-04-09" @default.
- W1499350750 modified "2023-09-25" @default.
- W1499350750 title "Lie-Rinehart algebras, Gerstenhaber algebras, and B-V algebras" @default.
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