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From Lie algebras to DG Lie algebras

  • Time 11/26/2020 6:00 PM - 11/26/2020 7:00 PM
  • Venue E403, Education Building of GTIIT
  • Speakers Prof. Jacob Mostovoi (GTIIT Mathematics with Computer Science Program)


There exist various non-trivial functors from the category of Lie algebras to the category of differential graded Lie algebras. As I will argue in this talk, such functors give rise to "homology theories" for Lie algebras; Chevalley-Eilenberg homology and Leibniz homology being the principal examples. I will also explain how Leibniz algebras can be thought of as a very particular subcategory of DG Lie algebras. There is also a non-linear version of this story which involves pre-crossed modules, racks and simplicial groups.



Jacob Mostovoy is on sabbatical leave from the Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV) in Mexico City, where he works as a researcher. He obtained his Master degree in Physics from the Moscow institute of Physics and Technology (MFTI) in 1993 and his PhD in Mathematics from the University of Edinburgh in 1997. His thesis, written under the supervision of Elmer G. Rees, was dedicated to the topology of the spaces of real algebraic cycles on projective varieties. Since 1998, he works in Mexico: from 1998 to 2008 at the National Autonomous University of Mexico (UNAM) and since 2008 at CINVESTAV. He supervised 3 PhD theses and is currently directing two doctoral students. His research interests include algebraic and low-dimensional topology, algebraic and differential geometry, homological and non-associative algebra. In particular, many of his works are dedicated to the algebraic objects which have geometric interpretations, such as braid groups of various kinds, cactus groups, multiplicative graphs and so on. He is a coauthor of a book on knot theory published by Cambridge University Press and of more than 30 research papers.





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