scholarly journals Quadratic algebras based on $$SL(NM)$$ elliptic quantum $$R$$-matrices

2021 ◽  
Vol 208 (2) ◽  
pp. 1156-1164
Author(s):  
I. A. Sechin ◽  
A. V. Zotov
Keyword(s):  
Quadratic Algebras ◽  
Elliptic Quantum

RATIONAL DEGENERATION OF ELLIPTIC QUADRATIC ALGEBRAS

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 773-779 ◽  
Author(s):  
ALEKSANDR V. ODESSKI
Keyword(s):  
Quadratic Algebras

scholarly journals Elliptic quantum groups and Baxter relations

2018 ◽  
Vol 12 (3) ◽  
pp. 599-647 ◽  
Author(s):  
Huafeng Zhang
Keyword(s):  
Quantum Groups ◽  
Elliptic Quantum

scholarly journals ALGEBRAS ASSOCIATED TO PSEUDO-ROOTS OF NONCOMMUTATIVE POLYNOMIALS ARE KOSZUL

2005 ◽  
Vol 15 (04) ◽  
pp. 643-648 ◽  
Author(s):  
DMITRI PIONTKOVSKI
Keyword(s):  
Hilbert Series ◽  
Necessary Condition ◽  
Quadratic Algebras ◽  
Noncommutative Polynomials

Quadratic algebras associated to pseudo-roots of noncommutative polynomials have been introduced by I. Gelfand, Retakh, and Wilson in connection with studying the decompositions of noncommutative polynomials. Later they (with S. Gelfand and Serconek) showed that the Hilbert series of these algebras and their quadratic duals satisfy the necessary condition for Koszulity. It is proved in this note that these algebras are Koszul.

scholarly journals Quasi-Hopf superalgebras and elliptic quantum supergroups

1999 ◽  
Vol 40 (10) ◽  
pp. 5264-5282 ◽  
Author(s):  
Yao-Zhong Zhang ◽  
Mark D. Gould
Keyword(s):  
Elliptic Quantum

scholarly journals Bihamiltonian Structures and Quadratic Algebras in Hydrodynamics and on Non-Commutative Torus

2004 ◽  
Vol 250 (3) ◽  
pp. 581-612 ◽  
Author(s):  
B. Khesin ◽  
A. Levin ◽  
M. Olshanetsky
Keyword(s):  
Quadratic Algebras

Families of quadratic algebras and Hilbert series

2005 ◽  
pp. 119-131
Author(s):  
Alexander Polishchuk ◽  
Leonid Positselski
Keyword(s):  
Hilbert Series ◽  
Quadratic Algebras
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