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1,013
Slinglend: Noncommutative ball maps
 J. Funct. Anal
"... Abstract In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrice ..."
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Cited by 14 (4 self)
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Abstract In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets
Classification of commutative algebras and tube realizations of hyperquadrics
, 2009
"... In this paper we classify up to affine equivalence all local tube realizations of real hyperquadrics in C^n. We show that this problem can be reduced to the classification, up to isomorphism, of commutative nilpotent real and complex algebras. We also develop some structure theory for commutative n ..."
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Cited by 7 (3 self)
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In this paper we classify up to affine equivalence all local tube realizations of real hyperquadrics in C^n. We show that this problem can be reduced to the classification, up to isomorphism, of commutative nilpotent real and complex algebras. We also develop some structure theory for commutative
A Deformation of Commutative Polynomial Algebras in Even Number of Variables
"... Abstract. We introduce and study a deformation of commutative polynomial algebras in even number of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right and left total symbols of differential ..."
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Cited by 2 (2 self)
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Abstract. We introduce and study a deformation of commutative polynomial algebras in even number of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right and left total symbols
A Note on Commutative Multivariate Rational Series
, 2003
"... Direct arguments are presented showing that for rational series in several commuting variables, the rational series problem is noncomputable, and closure under Hadamard product fails. ..."
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Direct arguments are presented showing that for rational series in several commuting variables, the rational series problem is noncomputable, and closure under Hadamard product fails.
Rationality in Algebras With a Series Operation
 Information and Computation
, 2000
"... . This paper considers languages in a free algebra which has a binary associative operation called the series product. We define automata operating in these algebras and rational expressions, and we show that their expressive powers coincide (a Kleene theorem). We also show that this expressive p ..."
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Cited by 16 (4 self)
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power equals that of algebraic recognizability (a MyhillNerode theorem). This generalizes the work of Thatcher and Wright. The first equivalence continues to hold when conditions such as associativity and commutativity are imposed on the term operations, but recognizability is weaker when one
Powers of the Euler product and commutative subalgebras of a complex simple Lie algebra
"... ABSTRACT. If g is a complex simple Lie algebra, and k does not exceed the dual Coxeter number of g, then the k th coefficient of the dim g power of the Euler product may be given by the dimension of a subspace of ∧ k g defined by all abelian subalgebras of g of dimension k. This has implications for ..."
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Cited by 27 (0 self)
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series in the variable x obtained from the expansion of the infinite product Π ∞ n=1(1 − x n). The Dedekind ηfunction is x 1/24 times the Euler product. Let g be a complex simple Lie algebra, and let K be a simply connected compact group such that k = Lie K is a compact form of g. Let ℓ
Computations in a Free Lie Algebra
, 1998
"... Many numerical algorithms involve computations in Lie algebras, like composition and splitting methods, methods involving the BakerCampbellHausdorff formula and the recently developed Lie group methods for integration of differential equations on manifolds. This paper is concerned with complexity ..."
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Cited by 62 (16 self)
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and optimization of such computations in the general case where the Lie algebra is free, i.e. no specific assumptions are made about its structure. It is shown how transformations applied to the original variables of a problem yield elements of a graded free Lie algebra whose homogeneous subspaces are of much
A Term Equality Problem Equivalent to Graph Isomorphism
 Information Processing Letters
, 1994
"... We demonstrate that deciding if two terms containing otherwise uninterpreted associative, commutative, and associativecommutative function symbols and commutative variablebinding operators are equal is polynomially equivalent to determining if two graphs are isomorphic. The reductions we use provi ..."
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Cited by 9 (1 self)
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We demonstrate that deciding if two terms containing otherwise uninterpreted associative, commutative, and associativecommutative function symbols and commutative variablebinding operators are equal is polynomially equivalent to determining if two graphs are isomorphic. The reductions we use
ALGEBRAS
"... A b s t r a c t. Formulas for computing the number of Df2algebra structures that can be defined over Bn, where Bn is the Boolean algebra with n atoms, as well as the fine spectrum of Df2 are obtained. Properties of the lattice of all subvarieties of Df2, Λ(Df2), are exhibited. In particular, the po ..."
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A b s t r a c t. Formulas for computing the number of Df2algebra structures that can be defined over Bn, where Bn is the Boolean algebra with n atoms, as well as the fine spectrum of Df2 are obtained. Properties of the lattice of all subvarieties of Df2, Λ(Df2), are exhibited. In particular
On Images of Algebraic Series
 J. Univ. Comput. Sci
, 1996
"... : We show that it is decidable whether or not the set of coefficients of a given Qalgebraic sequence is finite. The same question is undecidable for Qalgebraic series. We consider also prime factors of algebraic series. Category: F.4.3 1 Introduction Formal power series play an important role i ..."
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Cited by 3 (2 self)
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. In language theory formal power series often provide a powerful tool for obtaining deep decidability results, see [Kuich and Salomaa 86] and [Salomaa and Soittola 78]. A brilliant example is the solution of the equivalence problem for finite deterministic multitape automata given in [Harju and Karhumaki 91
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