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Coalgebras: Coalgebra, Lie coalgebra, F-coalgebra, Bialgebra, Quasi-bialgebra, Lie bialgebra, Quasi-Hopf algebra
Paperback. Books LLC 2010-05-29.
ISBN 9781157234791
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Förlagets beskrivning
Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Coalgebra, Lie Coalgebra, F-Coalgebra, Quasi-Bialgebra, Lie Bialgebra, Quasi-Hopf Algebra, Quasi-Triangular Quasi-Hopf Algebra, Quasi-Frobenius Lie Algebra, Comodule, Colinear Map. Excerpt: 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 arrows around, one obtains the axioms of coalgebras. Every coalgebra, by (vector space) duality, gives rise to an algebra, but not in general the other way. In finite dimensions, this duality goes in both directions (see below). Coalgebras occur naturally in a number of contexts (for example, universal enveloping algebras and group schemes). There are also F-coalgebras, with important applications in computer science. Formally, a coalgebra over a field K is a K-vector space C together with K-linear maps and such that (Here and refer to the tensor product over K.) Equivalently, the following two diagrams commute: In the first diagram we silently identify with ; the two are naturally isomorphic. Similarly, in the second diagram the naturally isomorphic spaces , and are identified. The first diagram is the dual of the one expressing associativity of algebra multiplication (called the coassociativity of the comultiplication); the second diagram is the dual of the one expressing the existence of a multiplicative identity. Accordingly, the map is called the comultiplication (or coproduct) of C and is the of C. In finite dimensions, the duality between algebras and coalgebras is closer: the dual of a finite-dimensional (unital associative) algebra is a coalgebra, while the dual of a finite-dimensional coalgebra is a (unital a... More: http://booksllc.net/?id=310886
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Coalgebras: Coalgebra, Lie coalgebra, F-coalgebra, Bialgebra, Quasi-bialgebra, Lie bialgebra, Quasi-Hopf algebra
Bokrecensioner » Coalgebras: Coalgebra, Lie coalgebra, F-coalgebra, Bialgebra, Quasi-bialgebra, Lie bialgebra, Quasi-Hopf algebra
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