SK1 of finite group rings: V.
Let τ be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category HHγD and there exists a Hopf algebra isomorphism w: B ∞ H → B [×]τ H in C, where B ∞ H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×]τ H is the Hopf algebra defined by Doi and Takeuchi.
En un trabajo de Huq se introduce el concepto de resolubilidad en categorías [2]. En mi tesis doctoral [1 (4.2.3), p.87] se hace distinción entre resolubilidad fuerte (resolubilidad de Huq) y resolubilidad, conceptos que coinciden en el caso de grupos, anillos asociativos y álgebras de Lie, pero no en cualquier tipo de Ω-grupos, donde la resolubilidad corresponde a la introducida en [1].El objeto de esta nota es dar una caracterización de los objetos resolubles (corolario 6), la cual nos permite...
Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable...
Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable ...