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Non-commutative differential calculus of some algebras of polynomial type having PBW bases
(Bogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2020-06-12)
In this work, we study the notion of differential calculus associated to an associative algebra, from its origin in manifolds geometry, to some generalizations in non commutative differential geometry. In particular, we ...
Algebraic quantum field theory and noncommutative moment problems I
(Pontificia Universidad Católica del PerúPE, 2017)
A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial TypeUn estudio sobre algunas caracterizaciones algebraicas del teorema de ceros de Hilbert para anillos no conmutativos de tipo polinomial
(Universidad EAFIT, 2020-06-19)
In this paper we present a survey of some algebraic characterizations of Hilbert’s Nullstellensatz for non-commutative rings of polynomial type. Using several results established in the literature, we obtain a version of ...
Noncommutative (generalized) sine-Gordon/massive Thirring correspondence, integrability and solitons
(Universidad Nacional de Ingeniería, 2019)
Noncommutative (generalized) sine-Gordon/massive Thirring correspondence, integrability and solitons
(Universidad Nacional de Ingeniería, 2019)
Zariski cancellation problem for skew PBW extensions
(Bogotá - Ciencias - Doctorado en Ciencias - MatemáticasDepartamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2020-06-19)
A special question for noncommutative algebras is Zariski cancellation problem. In this thesis we establish cancellation for some special classes of algebras such as skew PBW extensions, some Artin--Schelter regular algebras ...
Position-dependent noncommutativity in quantum mechanics
(AMER PHYSICAL SOC, 2009)
The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates [(x) over cap (i), (x) over cap (j)] = omega(ij) ((x) ...
N-Koszul algebras, Calabi-Yau algebras and skew PBW extensions
(2017-11-01)
Abstract. In the schematic approach to non-commutative algebraic geometry arises some important classes of non-commutative algebras like Koszul algebras, Artin-Schelter regular algebras, Calabi-Yau algebras, and closely ...
Some comments on the integrability of the noncommutative generalized massive Thirring model
(Sissa Medialab, 2009-12-14)