Hyperplane Face Semigroups and their Algebras.
Combinatorial Aspects of Hyperplane Arrangements
October 31,2004 09:30 AM to 10:30 AM
Speakers:
Brown, Ken
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Summary: |
The lecture surveys the face semigroup associated to a real hyperplane
arrangement. The Tsetlin library and the riffle shuffle are described and
used to motivate the study of random walks on the face semigroup. The
transition matrix of this random walk is diagonalizable with real
eigenvalues, which are described in terms of the intersection lattice of
the hyperplane arrangement, and we get an estimate of the rate of
convergence to stationarity. The semigroup algebra is an elementary
algebra, so it is a quotient of the path algebra of a quiver. It turns
out that for a hyperplane face semigroup this quiver is the Hasse diagram of
the intersection lattice (ordered by inclusion), with the arrows directed |
Keywords: |
Hyperplane arrangements; random walks; Markov chains; semigroups; bands; quivers. |
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Lecture #10711
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• 10711-Brown-.pdf (0.2 MB)
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