Details:
Title  Letterplace ideals and noncommutative Gröbner bases  Author(s)  Roberto La Scala, Viktor Levandovskyy  Type  Article in Journal  Abstract  In this paper we propose a 1to1 correspondence between graded twosided ideals of the free associative algebra and some class of ideals of the algebra of polynomials, whose variables are doubleindexed commuting ones. We call these ideals the “letterplace analogues” of graded twosided ideals. We study the behaviour of the generating sets of the ideals under this correspondence, and in particular that of the Gröbner bases. In this way, we obtain a new method for computing noncommutative homogeneous Gröbner bases via polynomials in commuting variables. Since the letterplace ideals are stable under the action of a monoid of endomorphisms of the polynomial algebra, the proposed algorithm results in an example of a Buchberger procedure “reduced by symmetry”. Owing to the portability of our algorithm to any computer algebra system able to compute commutative Gröbner bases, we present an experimental implementation of our method in Singular. By means of a representative set of examples, we show finally that our implementation is competitive with computer algebra systems that provide noncommutative Gröbner bases from classical algorithms.  Keywords  Free associative algebras, Gröbner bases, Monoid action, Invariant ideals  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717109000637 
Language  English  Journal  Journal of Symbolic Computation  Volume  44  Number  10  Pages  1374  1393  Year  2009  Edition  0  Translation 
No  Refereed 
No 
