|Thursday 4 March 2021|
|Events for day: Thursday 18 February 2021|
| 11:00 - 13:00 Commutative Algebra Webinar|
On the Homotopy Lie Algebra of a Graded Commutative Algebra
We give the definition of a graded Lie algebra with examples. The free Lie algebra on a set $X$ is defined and the enveloping algebra of quotients of free Lie algebras are studied. The Koszul dual is looked upon as the enveloping algebra of a Lie algebra in the graded commutative case with examples. The Poincare-Birkhoff-Witt theorem is stated and as a consequence, a formula for the Hilbert series of the enveloping algebra is obtained. In the graded commutative case a coproduct $Delta$ on $ext_A(k,k)$ is possible to define and thereby the homotopy Lie algebra is defined as the set of $x$ such that $Delta(x)=$reak $xotimes1+1otimes x$. ...