منابع مشابه
Gröbner Bases, Invariant Theory and Equivariant Dynamics
This paper is about algorithmic invariant theory as it is required within equivariant dynamical systems. The question of generic bifurcation equations (arbitrary equivariant polynomial vector) requires the knowledge of fundamental invariants and equivariants. We discuss computations which are related to this for finite groups and semi-simple Lie groups. We consider questions such as the complet...
متن کاملGröbner bases of ideals invariant under endomorphisms
We introduce the notion of Gröbner S-basis of an ideal of the free associative algebra K〈X〉 over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Gröbner S-bases of the ideal corresponding to the universal enveloping algebra of the free nilpotent of class 2 Lie algebra and of the T-ideal generated by the polynomial identity [x, y, z] = 0, w...
متن کاملMultiplicative Bases, Gröbner Bases, and Right Gröbner Bases
Before surveying the results of the paper, we introduce path algebras. Path algebras play a central role in the representation theory of finite-dimensional algebras (Gabriel, 1980; Auslander et al., 1995; Bardzell, 1997) and the theory of Gröbner bases (Bergman, 1978; Mora, 1986; Farkas et al., 1993) has been an important tool in some results (Feustel et al., 1993; Green and Huang, 1995; Bardze...
متن کاملCounting and Gröbner Bases
Gröbner bases were introduced by Buchberger (1965) and are now firmly established as a tool in Commutative Algebra and other areas. The reader is referred to Buchberger (1985), Cox, Little and O’Shea (1992) or Becker and Weispfenning (1993) for more information. Eisenbud (1995) places Gröbner bases within the context of more advanced Commutative Algebra. The ingredients for a Gröbner basis are ...
متن کاملRegular Gröbner Bases
In Ufnarovski (1989), the concept of automaton algebras is introduced. These are quotients of the non-commutative polynomial ring where the defining ideal allows some Gröbner basis with a regular set of leading words. However, nothing is reflected concerning the whole structure of the Gröbner basis (except of course for monomial algebras). In this paper we introduce the concept of regular Gröbn...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1989
ISSN: 0001-8708
DOI: 10.1016/0001-8708(89)90053-4