Talk
Speaker: Aditya Dwivedi, IIT Bombay
Host: Rekha Santhanam
Title: A généralisation of the HKR theorem for simplicial vector spaces.
Time, day and date: 11:00:00 AM – 12:00:00 PM, Friday, May 01
Venue: Room 215
Abstract: Hochschild homology, introduced by Hochschild in 1945 remains an important invariant of associative algebras. The theory of Associative algebras has connections to sevelars areas in commutative algebra, algebraic geometry and algebraic topology. In their 1962 paper, Hochschild, Konstant and Rosenberg proved a landmark result in this area which is now known as the HKR-theorem. Several generalisations have been done of the HKR theorem to highlight connections with the de Dham complex, Andre Quillen homology and cyclic homology.

In this talk, we present the work of Pirashvilli(2000) proving a version of HKR theorem for simplicial k vector spaces. The proof defined stable homotopy groups of such objects and the classical HKR theorem follows from the general case.