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SUMMARY:Quadratic algebras\, Yang-Baxter equation\, and Artin-Schelter reg
ularity
DTSTART;VALUE=DATE-TIME:20140613T090000Z
DTEND;VALUE=DATE-TIME:20140613T100000Z
DTSTAMP;VALUE=DATE-TIME:20210623T122447Z
UID:indico-event-454@indico.math.cnrs.fr
DESCRIPTION:We study two classes of n-generated quadratic algebras over a
field K. The first is the class Cn of all n-generated PBW algebras with po
lynomial growth and finite global dimension. We show that a PBW algebra A
is in Cn iff its Hilbert series is HA(z) = 1/(1-z)n. Furthermore each clas
s Cn contains a unique (up to isomorphism) monomial algebra A = K ‹ x1\,
… \, xn › / (xj xi | 1 ≤£ i < j £ n). The second is the class of
n-generated quantum binomial algebras A\, where the defining relations are
nondegenerate square-free binomials xy - cxy zt\, with nonzero coefficien
ts cxy. Our main result shows that the following conditions are equivalent
: (i) A is a Yang-Baxter algebra\, that is the set of quadratic relations
R defines canonically a solution of the Yang-Baxter equation. (ii) A is an
Artin-Schelter regular PBW algebra. (iii) A is a PBW algebra with polynom
ial growth. (iv) A is a binomial skew polynomial ring. (v) The Koszul dual
A! is a quantum Grassmann algebra.\n\nhttps://indico.math.cnrs.fr/event/4
54/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/454/
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