A universal enveloping for L ∞ - algebras
نویسنده
چکیده
For any L ∞-algebra L we construct an A ∞-algebra structure on the symmetric coalgebra Sym * c (L) and prove that this structure satifies properties generalizing those of the usual universal enveloping algebra. We also obtain an invariant contracting homotopy one the cobar construction of a symmetric coalgebra, by relating it to the combinatorics of permutahedra and semistandard Young tableaux.
منابع مشابه
Ideals in Non-associative Universal Enveloping Algebras of Lie Triple Systems
The notion of a non-associative universal enveloping algebra for a Lie triple system arises when Lie triple systems are considered as Bol algebras (more generally, Sabinin algebras). In this paper a new construction for these universal enveloping algebras is given, and their properties are studied. It is shown that universal enveloping algebras of Lie triple systems have surprisingly few ideals...
متن کاملThe Isomorphism Problem for Universal Enveloping Algebras of Lie Algebras
Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ∼= U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.
متن کاملTHE POSITIVE PART OF THE QUANTIZED UNIVERSAL ENVELOPING ALGEBRA OF TYPE AnAS A BRAIDED QUANTUM GROUP
The aim of this paper is to explain the bialgebra structure of the positive part of the quantized universal enveloping algebra (Drinfeld-Jimbo quantum group) of type Anusing the Lie algebra theory concepts. Recently has been introduced a generalization of Lie algebras, the basic T -Lie algebras [1]. Using the T -Lie algebra concept some new (we think) quantum groups of type Ancan be constructed...
متن کاملPrimeness of the Enveloping Algebra of a Cartan Type Lie Superalgebra
We show that a primeness criterion for enveloping algebras of Le superalgebras discovered by Bell is applicable to the Cartan type Lie superal-gebras W(n), n even. Other algebras are considered but there are no deenitive answers in these cases. Allen Bell has shown in B] that if L is a nite-dimensional Lie superalgebra over a eld of characteristic zero, then the primeness of the universal envel...
متن کاملDelta Methods in Enveloping Algebras of Lie Colour Algebras
In recent papers J. Bergen and D. S. Passman have applied so-called`Delta methods' to enveloping algebras of Lie superalgebras. This paper generalizes their results to the class of Lie colour algebras. The methods and results in this paper are very similar to those of Bergen and Passman, and many of their proofs generalize easily. However, at some points there are serious diiculties to overcome...
متن کامل