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75
More on Noncommutative Polynomial Identity Testing
"... We continue the study of noncommutative polynomial identity testing initiated by Raz and Shpilka and present efficient algorithms for the following problems in the noncommutative model: Polynomial identity testing: The algorithm gets as an input an arithmetic circuit with the promise that the polyno ..."
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sided error) and evaluates the circuit over the ring of matrices. In addition, we present query complexity lower bounds for identity testing and explore the possibility of derandomizing our algorithm. The analysis of our algorithm uses a noncommutative variant of the SchwartzZippel test. Minimizing algebraic
Commentary on “Towards a Noncommutative ArithmeticGeometric Mean Inequality”
"... In their paper, Recht and Ré have presented conjectures and consequences of noncommutative variants of the arithmetic meangeometric mean (AMGM) inequality for positive definite matrices. Let A1,..., An be a collection of positive semidefinite matrices and i1,..., ik be random indices in {1,..., n} ..."
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Cited by 3 (0 self)
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In their paper, Recht and Ré have presented conjectures and consequences of noncommutative variants of the arithmetic meangeometric mean (AMGM) inequality for positive definite matrices. Let A1,..., An be a collection of positive semidefinite matrices and i1,..., ik be random indices in {1,..., n
Noncommutative Disc Algebras For Semigroups
"... . We study noncommutative disc algebras associated to the free product of discrete subsemigroups of R + . These algebras are associated to generalized Cuntz algebras, which are shown to be simple and purely infinite. The nonselfadjoint subalgebras determine the semigroup up to isomorphism. Moreov ..."
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Cited by 6 (2 self)
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. We study noncommutative disc algebras associated to the free product of discrete subsemigroups of R + . These algebras are associated to generalized Cuntz algebras, which are shown to be simple and purely infinite. The nonselfadjoint subalgebras determine the semigroup up to isomorphism
NONCOMMUTATIVE MIXMASTER COSMOLOGIES
, 1203
"... Abstract. In this paper we investigate a variant of the classical mixmaster universe model of anisotropic cosmology, where the spatial sections are noncommutative 3tori. We consider ways in which the discrete dynamical system describing the mixmaster dynamics can be extended to act on the noncommut ..."
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Abstract. In this paper we investigate a variant of the classical mixmaster universe model of anisotropic cosmology, where the spatial sections are noncommutative 3tori. We consider ways in which the discrete dynamical system describing the mixmaster dynamics can be extended to act
De Rham and infinitesimal cohomology in Kapranov’s model for noncommutative algebraic geometry
, 2001
"... The title refers to the nilcommutative or NCschemes introduced by M. Kapranov in Noncommutative geometry based on commutator expansions, J. reine angew. Math 505 (1998) 73118. The latter are noncommutative nilpotent thickenings of commutative schemes. We consider also the parallel theory of nilP ..."
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Cited by 3 (2 self)
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of the infinitesimal site introduced by Grothendieck in Crystals and the de Rham cohomology of schemes, Dix exposés sur la cohomologie des schémas, Masson & Cie, NorthHolland (1968) 306358. It turns out that each of these noncommutative variants admits a kind of Hodge decomposition which allows one to express
Variants of aTmenability for actions on noncommutative Lpspaces
, 2013
"... We investigate various characterizations of the Haagerup property (H) for a second countable locally compact group G, in terms of orthogonal representations of G on Lp(M), the noncommutative Lpspace associated with the von Neumann algebra M. For a semifinite von Neumann algebra M, we introduce a ..."
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We investigate various characterizations of the Haagerup property (H) for a second countable locally compact group G, in terms of orthogonal representations of G on Lp(M), the noncommutative Lpspace associated with the von Neumann algebra M. For a semifinite von Neumann algebra M, we introduce a
Noncommutative variations on Laplace’s equation
 ANAL. PDE
, 2008
"... As a first step toward developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace’s equation and its variants (some of them nonlinear) over noncommutative tori. Along the way we prove noncommutative analogues of many result ..."
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Cited by 9 (4 self)
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As a first step toward developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace’s equation and its variants (some of them nonlinear) over noncommutative tori. Along the way we prove noncommutative analogues of many
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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of D'Angelo on such analytic maps in C. Another mathematically natural class of maps carries a variant of the noncommutative distinguished boundary to the boundary, but on these our results are limited. We shall be interested in several types of noncommutative balls, conventional ones, but also
H∞ FUNCTIONAL CALCULUS AND SQUARE FUNCTIONS ON Noncommutative L^Pspaces
, 2006
"... In this work we investigate semigroups of operators acting on noncommutative L pspaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H ∞ functional calculus. We discuss several examples of noncommutative diffusion semig ..."
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Cited by 30 (13 self)
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In this work we investigate semigroups of operators acting on noncommutative L pspaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H ∞ functional calculus. We discuss several examples of noncommutative diffusion
The Shuffle Hopf Algebra and Noncommutative Full Completeness
, 1999
"... We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformati ..."
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Cited by 9 (3 self)
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We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces
Results 1  10
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