Abstract
In the first chapter, we dealt only with Lie algebra deformations. Here, for differentiable deformations, it will be appropriate to treat also deformations of associative algebras - which of course will generate Lie algebra deformations. The theory of deformations for associative algebras follows exactly the same pattern as for Lie algebras, the connection with the second and third (associative algebra) Hochschild cohomology groups, the algebra acting on itself by left and right multiplication, being the same; so we shall not repeat it. (Actually the original paper of Gerstenhaber [2] was formulated in the associative algebra context, with a remark that the Lie algebra case was similar.) The main difference is that these groups are so large in the associative case that it is then even more difficult to obtain concrete results.
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Notes and references to chapters 1 and 2
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© 1980 D. Reidel Publishing Company, Dordrecht, Holland
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Flato, M., Sternheimer, D. (1980). Differentiable Deformations of the Poisson Bracket Lie Algebra. In: Wolf, J.A., Cahen, M., De Wilde, M. (eds) Harmonic Analysis and Representations of Semisimple Lie Groups. Mathematical Physics and Applied Mathematics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8961-0_10
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DOI: https://doi.org/10.1007/978-94-009-8961-0_10
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