comultiplication
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Bialgebra — In mathematics, a bialgebra over a field K is a structure which is both a unital associative algebra and a coalgebra over K , such that these structures are compatible.Compatibility means that the comultiplication and the counit are both unital… … Wikipedia
Coalgebra — In mathematics, coalgebras or cogebras are structures that are dual (in the sense of reversing arrows) to unital associative algebras. The axioms of unital associative algebras can be formulated in terms of commutative diagrams. Turning all… … Wikipedia
Quantum group — In mathematics and theoretical physics, quantum groups are certain noncommutative algebras that first appeared in the theory of quantum integrable systems, and which were then formalized by Vladimir Drinfel d and Michio Jimbo. There is no single … Wikipedia
Compact quantum group — In mathematics, a compact quantum group is an abstract structure on a unital separable C* algebra axiomatized from those that exist on the commutative C* algebra of continuous complex valued functions on a compact quantum group. The basic… … Wikipedia
Lie bialgebra — In mathematics, a Lie bialgebra is the Lie theoretic case of a bialgebra: its a set with a Lie algebra and a Lie coalgebra structure which are compatible. It is a bialgebra where the comultiplication is skew symmetric and satisfies a dual Jacobi… … Wikipedia
Hopf algebra — In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra, a coalgebra, and has an antiautomorphism, with these structures compatible.Hopf algebras occur naturally in algebraic… … Wikipedia
Comodule — In mathematics, a comodule or corepresentation is a concept dual to a module. The definition of a comodule over a coalgebra is formed by dualizing the definition of a module over an associative algebra. Formal definition Let K be a field, and C… … Wikipedia
Steenrod algebra — In algebraic topology, a branch of mathematics, the Steenrod algebra is a structure occurring in the theory of cohomology operations. It is an object of great importance, most especially to homotopy theorists. More precisely, for a given prime… … Wikipedia
Lógica probabilística — El objetivo de una lógica probabilística (o la lógica de probabilidad) debe combinar la capacidad de teoría de probabilidad para manejar la incertidumbre con la capacidad de lógica deductiva para explotar la estructura. El resultado es un… … Wikipedia Español
Associative algebra — In mathematics, an associative algebra is a vector space (or more generally, a module) which also allows the multiplication of vectors in a distributive and associative manner. They are thus special algebras. Definition An associative algebra A… … Wikipedia
