Idempotent solutions of the Yang–Baxter equation and twisted group division

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

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Trace and determinant in algebras associated with the yang-baxter equation

Functional Analysis and Its Applications ◽

10.1007/bf02577142 ◽

1987 ◽

Vol 21 (3) ◽

pp. 239-240

Author(s):

D. I. Gurevich

Keyword(s):

Baxter Equation

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Semi-Prime Twisted Group Rings

Journal of the London Mathematical Society ◽

10.1112/jlms/s2-12.4.413 ◽

1976 ◽

Vol s2-12 (4) ◽

pp. 413-418 ◽

Cited By ~ 7

Author(s):

A. Reid

Keyword(s):

Group Rings ◽

Twisted Group

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Ore extensions of quasitriangular Hopf group coalgebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498814500169 ◽

2014 ◽

Vol 13 (06) ◽

pp. 1450016 ◽

Cited By ~ 1

Author(s):

Daowei Lu ◽

Dingguo Wang

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Baxter Equation ◽

Ore Extension ◽

Ore Extensions ◽

Necessary And Sufficient

In this paper, we mainly consider some special Ore extension of quasitriangular Hopf group coalgebra, and give the necessary and sufficient conditions when the Ore extension of quasitriangular Hopf group coalgebras will preserve the same quasitriangular structure. Furthermore, in the two examples given at the end, we construct new solutions of Yang–Baxter equation of Hopf group coalgebras version.

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