Simplex equations and their solutions

Igor Frenkel; Gregory Moore

doi:10.1007/BF02099492

Simplex equations and their solutions

Igor Frenkel
, Gregory Moore

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

We investigate an n-simplex generalization of the classical and quantum Yang-Baxter equation. For the case of sl(2) we find the most general solution of the classical n-simplex equation for all n. These classical solutions can be quantized (in the sense of quantum group theory) for n=2,3 and we exhibit a quantum solution to the tetrahedron equations (n=3). The classical nondegenerate solutions cannot be quantized for n=4.

Original language	American English
Pages (from-to)	259-271
Number of pages	13
Journal	Communications In Mathematical Physics
Volume	138
Issue number	2
DOIs	https://doi.org/10.1007/BF02099492
State	Published - May 1 1991
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02099492

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title = "Simplex equations and their solutions",

abstract = "We investigate an n-simplex generalization of the classical and quantum Yang-Baxter equation. For the case of sl(2) we find the most general solution of the classical n-simplex equation for all n. These classical solutions can be quantized (in the sense of quantum group theory) for n=2,3 and we exhibit a quantum solution to the tetrahedron equations (n=3). The classical nondegenerate solutions cannot be quantized for n=4.",

author = "Igor Frenkel and Gregory Moore",

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AU - Moore, Gregory

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N2 - We investigate an n-simplex generalization of the classical and quantum Yang-Baxter equation. For the case of sl(2) we find the most general solution of the classical n-simplex equation for all n. These classical solutions can be quantized (in the sense of quantum group theory) for n=2,3 and we exhibit a quantum solution to the tetrahedron equations (n=3). The classical nondegenerate solutions cannot be quantized for n=4.

AB - We investigate an n-simplex generalization of the classical and quantum Yang-Baxter equation. For the case of sl(2) we find the most general solution of the classical n-simplex equation for all n. These classical solutions can be quantized (in the sense of quantum group theory) for n=2,3 and we exhibit a quantum solution to the tetrahedron equations (n=3). The classical nondegenerate solutions cannot be quantized for n=4.

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U2 - 10.1007/BF02099492

DO - 10.1007/BF02099492

M3 - Article

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VL - 138

SP - 259

EP - 271

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 2

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Simplex equations and their solutions

Abstract

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