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The structure of smooth algebras in Kapranov's framework for noncommutative geometry
(Academic Press Inc Elsevier Science, 2004-11)
In Kapranov, M. Noncommutative geometry based on commutator expansions, J. reine angew. Math 505 (1998) 73-118, a theory of noncommutative algebraic varieties was proposed. Here we prove a structure theorem for the ...
States in generalized probabilistic models: An approach based in algebraic geometry
(De Gruyter, 2019-06)
We present a characterization of states in generalized probabilistic models by appealing to a non-commutative version of geometric probability theory based on algebraic geometry techniques. Our theoretical framework allows ...
Connes' metric for states in group algebras
(Unión Matemática Argentina, 2003-12)
We follow the main idea of A. Connes for the construction of a metric in the state space of a C*-algebra. We focus in the reduced algebra of a discrete group Г, and prove some equivalences and relations between two central ...
Twisted Semigroup Algebras
(Springer, 2015-08)
We study 2-cocycle twists, or equivalently Zhang twists, of semigroup algebras over a field k. If the underlying semigroup is affine, that is abelian, cancellative and finitely generated, then Spec k[S] is an affine toric ...
Noncommutativity in (2+1)-dimensions and the Lorentz group
(American Physical Society, 2012-11)
In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible ...
Quantum toric degeneration of quantum flag and Schubert varieties
(Springer, 2020-09)
We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative ...
Evolution of quantum observables: from non-commutativity to commutativity
(Springer, 2020-07)
A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. ...
Quantum function algebras from finite-dimensional Nichols algebras
(European Mathematical Society, 2020-10)
We describe how to find quantum determinants and antipode formulas from braidedvector spaces using the FRT-construction and finite-dimensional Nichols algebras. It improvesthe construction of quantum function algebras using ...
Cyclic homology of monogenic extensions in the noncommutative setting
(Academic Press Inc Elsevier Science, 2009-01-15)
We study the Hochschild and cyclic homology of noncommutative monogenic extensions. As an application we compute the Hochschild and cyclic homology of the rank 1 Hopf algebras introduced in [L. Krop, D. Radford, Finite ...
Projective modules and Gröbner bases for skew PBW extensions
(Polish Academy of Sciences. Institute of Mathematics, 2017-01)
Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincare- Birkhoff Witt) extensions. In the present paper we study two aspects ...