STRONG DUALITY, RIGIDITY AND PREFERRED DEFORMATIONS. P. BONNEAU 1 M. FLATO1, M. GERSTENHABER 2 and G. PINCZON 1 Abstract: A notion of well-behaved Hopf algebra is introduced; re exivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coe cients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all gener...

In this paper we present a novel approach to the construction of new finite algebras and describe the congruence lattices of these algebras. Given a finite algebra 〈B, . . .〉, let B1, B2, . . . , BK be sets which intersect B at specific points. We construct an overalgebra 〈A,FA〉, by which we mean an expansion of 〈B, . . .〉 with universe A := B ∪ B1 ∪ · · · ∪ BK , and a certain set FA of unary o...

In the present paper, by considering the notion of ideals in $MV$-algebras, we study some kinds of ideals in $MV$-algebras and obtain some results on them. For example, we present definition of ultra ideal in $MV$-algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$...

The search for higher homotopy Hopf algebras (known today as A∞-bialgebras) began in 1996 during a conference at Vassar College honoring Jim Stasheff in the year of his 60th birthday. In a talk entitled ”In Search of Higher Homotopy Hopf Algebras”, I indicated that a DG Hopf algebra could be thought of as some (unknown) higher homotopy structure with trivial higher order structure and deformed ...

The main motivation for the study of cluster algebras initiated in [4, 6, 1] was to design an algebraic framework for understanding total positivity and canonical bases in semisimple algebraic groups. In this paper, we introduce and explicitly construct the canonical basis for a special family of cluster algebras of rank 2. ju-bi-lee 1 : a year of emancipation and restoration provided by ancien...

Abstract We prove that the category $\mathsf {SBor}$ of standard Borel spaces is (bi-)initial object in 2-category countably complete Boolean (countably) extensive categories. This means universal admitting some familiar algebraic operations countable arity (e.g., products and unions) obeying simple compatibility conditions distribute over disjoint unions). More generally, for any infinite regu...