## 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

### Keywords:

universal enveloping algebra functor

Zbl 0801.55004
Full Text:

### References:

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