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Strongly homotopy Lie algebras. (English) Zbl 0999.17019

The authors obtain a correspondence between \(A(m)\) (associative algebra) and \(L(m)\) (Lie algebra) structures on a graded vector space, generalizations of the universal enveloping algebra functor. They investigate the notion of universal enveloping \(A(m)\)-algebra of an \(L(m)\)-algebra and prove a one-to-one correspondence between \(L\)-module structures on a graded differential vector space \(M\) and weak \(L(m)\)-maps \(L\to \operatorname {End}M_L\), \(L\) a graded vector space having \(L(m)\)-structure.
See the second author’s paper in J. Pure Appl. Algebra 83, 141-175 (1992; Zbl 0801.55004) for motivation of this study.

MSC:

17B35 Universal enveloping (super)algebras
16S30 Universal enveloping algebras of Lie algebras
18G60 Other (co)homology theories (MSC2010)
55P62 Rational homotopy theory

Citations:

Zbl 0801.55004
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References:

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