Simultaneous representations in discrete structures
Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let and be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of . As a corollary, we find that if and only if if and only if .
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...