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Finite dimensional semigroup quadratic algebras with the minimal number of relations.
- Source :
- Monatshefte für Mathematik; Nov2012, Vol. 168 Issue 2, p239-252, 14p
- Publication Year :
- 2012
-
Abstract
- A quadratic semigroup algebra is an algebra over a field given by the generators x, . . . , x and a finite set of quadratic relations each of which either has the shape x x = 0 or the shape x x = x x. We prove that a quadratic semigroup algebra given by n generators and $${d\leq \frac{n^2+n}{4}}$$ relations is always infinite dimensional. This strengthens the Golod-Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and δ relations, where δ is the first integer greater than $${\frac{n^2+n}{4}}$$ . That is, the above Golod-Shafarevich-type estimate for semigroup algebras is sharp. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00269255
- Volume :
- 168
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Monatshefte für Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 82504941
- Full Text :
- https://doi.org/10.1007/s00605-011-0339-8