scholarly journals Quadratic Algebras and Integrable Chains

2009 ◽  
Author(s):  
F. Soloviev
Keyword(s):  
Quadratic Algebras ◽  
Integrable Chains

RATIONAL DEGENERATION OF ELLIPTIC QUADRATIC ALGEBRAS

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

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.

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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