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CATEGORIES:Lecture, Colloquia, Seminar
DESCRIPTION:Speaker: Rina Anno (KSU)\n\nAbstract: Let A be a DG algebra or
a small DG category. Let H_1\, ... H_n be objects in the derived category D
(A-A) of A-A bimodules that satisfy the braid-like relation $H_i \otimes H_
j \otimes H_i \simeq H_j\otimes H_i \otimes H_j$ for |i-j|=1. Then we can c
onstruct a certain algebra object in D(A-A). When A is commutative and each
H_i is isomorphic to A\, this gives the usual nil Hecke algebra over A\; o
verall\, this construction is best thought of as the nil Hecke algebra wher
e the generators don't necessarily commute with the coefficients. This alge
bra has a collection of subalgebras enumerated by ordered partitions of $n$
. If H_i's are invertible in the monoidal category D(A-A)\, the derived cat
egories of representations of these subalgebras are equivalent whenever the
corresponding partitions differ by a permutation\, and those equivalences
generate (colored) braid group actions. We use this construction to show th
at any (DG-enhanceable) braid group action on a triangulated category can b
e completed to an action of a bigger diagrammatic category that we call the
category of generalized braids. This talk is based on an ongoing project w
ith Timothy Logvinenko.
DTEND:20200409T220000Z
DTSTAMP:20201127T232355Z
DTSTART:20200409T203000Z
LOCATION:
SEQUENCE:0
SUMMARY:M-Seminar: Nil Hecke algebra in the category of bimodules
UID:tag:localist.com\,2008:EventInstance_33180292730315
URL:https://events.k-state.edu/event/m-seminar_nil_hecke_algebra_in_the_cat
egory_of_bimodules
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