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Laura Skew Group Algebras
(Taylor & Francis, 2007-07)
We prove that if A is an artin algebra, G is a finite group acting on A such that |G| is invertible in A, and R=A[G]b is a basic algebra associated with the skew group algebra, then A is left supported (or right supported, ...
Partial actions of inverse semigroups and their associated algebras
(2018)
Estudamos a interação entre álgebras de Steinberg e skew álgebras de grupos parciais e caracterizamos isomorfismos de skew álgebras de grupos que preservam diagonal, sobre álgebras comutativas, em termos de equivalência ...
FREE GROUP ALGEBRAS IN DIVISION RINGS
(WORLD SCIENTIFIC PUBL CO PTE LTDSINGAPORE, 2012)
Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the ...
A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS
(TAYLOR & FRANCIS INC, 2009)
Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D ...
A view toward the geometry of normalizing sequences in finitely semi-graded algebras
(Bogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2020-05-15)
En este trabajo vemos el comportamiento de la sucesión normalizadora en
álgebras semi-graduadas. Primero, definimos la sucesión regular y el complejo de Koszul
en el caso conmutativo. Usando la variedad de ideales máximos, ...
Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
(World Scientific, 2019-09)
Using Bieberbach groups, we study multipermutation involutive solutions to the Yang-Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in ...
On Nichols algebras of diagonal type
(de Gruyter, 2013-11)
We give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. ...
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 ...
Associated prime ideals of noncommutative rings of polynomials type
(Departamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2019-10)
En el presente trabajo estudiamos los ideales primos asociados de algunos anillos no conmutativos de tipo polinomial. En la literatura encontramos que estos ideales fueron caracterizados en un primer trabajo por Brewer y ...
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 ...