Homogeneous algebras, statistics and combinatorics

DOI10.1023/A:1020770601601zbMath1020.16007arXivmath/0207085OpenAlexW2999032351MaRDI QIDQ1868237

Todor Popov, Michel Dubois-Violette

Publication date: 27 April 2003

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0207085

zbMATH Keywords

dualitiesYoung tableauxcomplexesArtin-Schelter regular algebrasquadratic algebrasKoszul algebrasplactic algebrashomogeneous algebrasparafermionic algebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Noncommutative geometry in quantum theory (81R60) Noncommutative geometry (à la Connes) (58B34) Quadratic and Koszul algebras (16S37)

Related Items (13)

Quantum Plactic and Pseudo-Plactic Algebras ⋮ Automorphisms of cubic algebras. ⋮ Koszul calculus for \(N\)-homogeneous algebras ⋮ Generalized down-up algebras revisited from a viewpoint of Gröbner basis theory ⋮ A numerical criterion for the generalized Koszul property. ⋮ \({\mathsf{N}}\)-complexes as functors, amplitude cohomology and fusion rules ⋮ Multilinear forms and graded algebras ⋮ Koszul and Gorenstein properties for homogeneous algebras. ⋮ Stability of the Koszul property for the semi-cross product of homogeneous algebras. ⋮ COMBINATORICS AND N-KOSZUL ALGEBRAS ⋮ PARASTATISTICS ALGEBRA, YOUNG TABLEAUX AND THE SUPER PLACTIC MONOID ⋮ Graded algebras and multilinear forms. ⋮ Aspects of a new class of braid matrices: Roots of unity and hyperelliptic q for triangularity, L-algebra, link-invariants, noncommutative spaces

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