- Speaker：Prof. Pavel Kolesnikov（Sobolev Institute of Mathematics,Russia）
- Time：2021.11.10 16:00
- Location：online
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Meeting ID: 968 6768 6894
Password: 211110
Speaker: Prof. Pavel Kolesnikov（Sobolev Institute of Mathematics,Russia）
Time: 16:00-17:00 Beijing time (11:00-12:00 Moscow time)
Abstract: Novikov algebras initially appeared in the study of Poisson brackets and, independently, in formal variational calculus.The operad Nov governing the variety of Novikov algebras turns out to be useful in the following general construction.Given a class Var of linear algebras with a family of binary operations (e.g., associative, alternative, Jordan, or Lie algebras, Poisson algebras) equipped with a derivation, one may construct a derived class of systems based on the same linear spaces relative to new operations: $x\prec y = xd(y)$, $x\succ y = d(x)y$, where $d$ is the derivation. What are the identities that hold on all such systems? We will show that the corresponding operad may be obtained as a Manin white product of operads Var and Nov. As an example, we define non-commutative analogues of Novikov algebras via the derived operad of associative algebras. We will prove that every noncommutative Novikov algebra embeds into an appropriate associative differential algebra.
Bio: Pavel Kolesnikov got his PhD in 2002 in Novosibirsk State University and joined Sobolev Institute of Mathematics. Since 2009 he occupies the Head of Laboratory position of this institute. As a part-time job, he is a professor of Novosibirsk State University. He also visited Korea Institute of Advanced Study, University of California in San Diego, University of Sao Paulo with research and teaching positions. His main area of research interests is in the structure and combinatorial theory of associative and non-associative algebras, conformal and vertex algebras.
