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A New Class of Algebraic Series Having a Decidable Equivalence Problem
"... We introduce a new class of algebraic series with noncommuting variables having a decidable equivalence problem. As a tool we consider star roots of formal power series. Keywords: Algebraic series, equivalence problem TUCS Research Group ..."
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We introduce a new class of algebraic series with noncommuting variables having a decidable equivalence problem. As a tool we consider star roots of formal power series. Keywords: Algebraic series, equivalence problem TUCS Research Group
FRÉCHET ALGEBRAS OF POWER SERIES
"... We consider Fréchet algebras which are subalgebras of the algebra F = C [[X]] of formal power series in one variable and of Fn = C [[X1,..., Xn]] of formal power series in n variables where n ∈ N. In each case, these algebras are taken with the topology of coordinatewise convergence. We begin with ..."
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Cited by 3 (3 self)
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problem for commutative Fréchet algebras has been described by Dixon and Esterle. We prove that there is an embedding of U into F, and so there is a Fréchet algebra of power series which is a test case for Michael’s problem. We also discuss homomorphisms from Fréchet algebras into F. We prove that such a
ON DEFORMATIONS OF COMMUTATION RELATION ALGEBRAS
, 1995
"... This paper is on C symmetric creation and annihilation operators, which are constructed on Wick’s algebras which fulfil consistency conditions. The essential assumption is that every algebraic action must be constant on equivalence classes. All consistency conditions follow from the above assumptio ..."
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This paper is on C symmetric creation and annihilation operators, which are constructed on Wick’s algebras which fulfil consistency conditions. The essential assumption is that every algebraic action must be constant on equivalence classes. All consistency conditions follow from the above
Positivity Problems and Conjectures in Algebraic Combinatorics
 in Mathematics: Frontiers and Perspectives
, 1999
"... Introduction. Algebraic combinatorics is concerned with the interaction between combinatorics and such other branches of mathematics as commutative algebra, algebraic geometry, algebraic topology, and representation theory. Many of the major open problems of algebraic combinatorics are related to p ..."
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Cited by 67 (1 self)
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Introduction. Algebraic combinatorics is concerned with the interaction between combinatorics and such other branches of mathematics as commutative algebra, algebraic geometry, algebraic topology, and representation theory. Many of the major open problems of algebraic combinatorics are related
Modeles Avec Particules Dures, Animaux Diriges, Et Series En Variables Partiellement Commutatives
"... We give a systematic presentation of relations between lattice gas models with hardcore interactions, enumeration of directedsite animals, and the algebra of formal powerseries in the partially commutative case, along the work of X.G.Viennot. We present a complete and simplified solution, using t ..."
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Cited by 18 (0 self)
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We give a systematic presentation of relations between lattice gas models with hardcore interactions, enumeration of directedsite animals, and the algebra of formal powerseries in the partially commutative case, along the work of X.G.Viennot. We present a complete and simplified solution, using
Equivalents of the KadisonSinger Problem
"... In a series of papers it was recently shown that the 1959 KadisonSinger Problem in C∗Algebras is equivalent to fundamental unsolved ..."
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Cited by 2 (0 self)
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In a series of papers it was recently shown that the 1959 KadisonSinger Problem in C∗Algebras is equivalent to fundamental unsolved
Invariant subspaces and hyperreflexivity for free semigroup algebras
 PROC. LONDON MATH. SOC. 78
, 1999
"... In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in term ..."
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Cited by 104 (23 self)
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in terms of the invariant subspaces. Such algebras are called hyperreflexive. This property is very strong, but it has been established in only a very few cases. Moreover the prototypes of this class of algebras are the natural candidate for a noncommutative analytic Toeplitz algebra on n variables
Commutation Problems on Sets of Words and Formal Power Series
, 2002
"... We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generaliza ..."
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Cited by 6 (3 self)
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We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural
Peak reduction technique in commutative algebra
, 1999
"... The “peak reduction” method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning ..."
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concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well. In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative
ON META.NORMAL FORMS FOR ALGEBRAIC POWER SERIES IN NONCOMMUTING VARIABLES
"... 1. Introiluction and preliminaries. The theory of formal power series in noncommuting variables was initiated around 1960 apart from some scattered work done earlier in connection with free groups. Such power series are applicable in a number of areas but, in particular, they have turned out to be ..."
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1. Introiluction and preliminaries. The theory of formal power series in noncommuting variables was initiated around 1960 apart from some scattered work done earlier in connection with free groups. Such power series are applicable in a number of areas but, in particular, they have turned out
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