Hall 123

On Multiplicative Lie Algebras

Mani Shankar Pandey

Institute of Mathematical Sciences

A multiplicative Lie algebra is a group a (G, ·), endowed with an additional binary operation ⋆ satisfying the identities similar to universal
commutator identities. The extra binary operation ⋆ on G is called the
multiplicative Lie product. On a non-abelian group G, the operations G×G
to G given by commutators ((x, y) 7→ xyx−1
y
−1
) or the constant map to
the identity ((x, y) 7→ 1) are examples of multiplicative Lie products. So,
it will be interesting to characterize the distinct multiplicative Lie products on a group. In my talk, I will present a partial characterization of
multiplicative Lie products on a finite group