scholarly journals Integrating a generic algebra

1998 ◽  
pp. 332-337
Author(s):  
R. Casalbuoni
Keyword(s):  
Generic Algebra

scholarly journals A generic algebra associated to certain Hecke algebras

2004 ◽  
Vol 278 (2) ◽  
pp. 502-531 ◽  
Author(s):  
Stephen Doty ◽  
Karin Erdmann ◽  
Anne Henke
Keyword(s):  
Hecke Algebras ◽  
Generic Algebra

scholarly journals Integration Over a Generic Algebra

1997 ◽  
Vol 12 (32) ◽  
pp. 5803-5826 ◽  
Author(s):  
R. Casalbuoni
Keyword(s):  
Path Integral ◽  
Configuration Spaces ◽  
Integral Formalism ◽  
Explicit Algorithm ◽  
Path Integral Formalism ◽  
Generic Algebra ◽  
Definition Of ◽  
General Conditions

In this paper we consider the problem of quantizing theories defined over configuration spaces described by noncommuting parameters. If one tries to do that by generalizing the path-integral formalism, the first problem one has to deal with is the definition of integral over these generalized configuration spaces. This is the problem we state and solve in the present work, by constructing an explicit algorithm for the integration over a generic algebra. The general conditions a given algebra has to satisfy in order to admit our integration are not yet fully understood, but many examples are discussed in order to illustrate our construction.

scholarly journals The Golod-Shafarevich inequality for Hilbert series of quadratic algebras and the Anick conjecture

2011 ◽  
Vol 141 (3) ◽  
pp. 609-629 ◽  
Author(s):  
Natalia Iyudu ◽  
Stanislav Shkarin
Keyword(s):  
Commutative Algebra ◽  
Hilbert Series ◽  
Infinite Field ◽  
Asymptotic Results ◽  
Quadratic Algebras ◽  
Princeton University ◽  
Number Of Generators ◽  
Finite Dimensional ◽  
Generic Algebra ◽  
Generic Algebras

We study the question of whether the famous Golod-Shafarevich estimate, which gives a lower bound for the Hilbert series of a (non-commutative) algebra, is attained. This question was considered by Anick in his 1983 paper, ‘Generic algebras and CW-complexes’ (Princeton University Press), where he proved that the estimate is attained for the number of quadratic relations d ≤ ¼n2 and d ≥ ½n2, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to ½n(n – 1) was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional.We prove that over any infinite field, the Anick conjecture holds for d ≥ (n2 + n) and an arbitrary number of generators n, and confirm the Vershik conjecture over any field of characteristic 0. We give also a series of related asymptotic results.

scholarly journals On dimension functions of the generic algebra of type Dn

1977 ◽  
Vol 45 (2) ◽  
pp. 435-438 ◽  
Author(s):  
Clark T Benson ◽  
David A Gay
Keyword(s):  
Generic Algebra ◽  
Dimension Functions
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