Michiel Hazewinkel, Introductory recommendations for the study of Hopf algebras in mathematics and physics, CWI Quarterly 4:1 (1991), 3--26. Home/Search Document Not in Database Summary Related Articles Check |
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The Shuffle Hopf Algebra and Noncommutative Full Completeness - Blute, Scott (1996) (5 citations) (Correct)
....then generalized and given a Hopf algebraic interpretation by Schmitt in [34] Thus the representation theory of such structures should have important consequences for both these subjects. An overview of the applications of Hopf algebras to various branches of mathematics is given by Hazewinkel in [21]. These results were first presented at the conference Linear Logic 96 at Keio University in Tokyo. An extended electronic abstract announcing the results has appeared as [14] Note to the Reader: To avoid repetition of previous work, we assume that the reader has some familiarity with Hopf ....
....from sequentialization for Yetter s nets, cf. 31] and the planarity condition described above. 2 5 Hopf algebras and Representations 5.1 Algebras and Coalgebras In this section we give a quick summary of the necessary background in bialgebras and Hopf algebras. For suitable introductions, see [1, 35, 21]. Definition 5.1 A Hopf algebra is a k vector space y , H, equipped with an algebra structure and a compatible coalgebra structure ( bialgebra) and an antipode satisfying the appropriate equations [21, 35] The following chart summarizes the necessary structure. All maps shown are linear. y ....
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M. Hazewinkel, Introductory Recommendations for the Study of Hopf Algebras in Mathematics and Physics, CWI Quarterly, Centre for Mathematics and Computer Science, Amsterdam Vol. 4, No. 1, March 1991.
Multiparameter Quantum Supergroups - Hazewinkel Self-citation (Hazewinkel) (Correct)
....standard matrix function algebra comultiplication j 7 t k Omega k j (1.3) where the Einstein summation convention is in force, i.e. on the righthand side of (1.3) a sum over k is implied. This makes K t a bialgebra and it is always the case that I(R) is a bialgebra ideal; cf e.g. [4] for a proof. Thus Kn (R) K t =I(R) 1.4) inherits a bialgebra structure. This is sometimes called the FRT construction (Faddeev Reshetikin Taktadzhyan) It was also indepedently noticed by other authors. Relations like (1.1) first came up in the work of the Faddeev group in what was ....
Michiel Hazewinkel, Introductory recommendations for the study of Hopf algebras in mathematics and physics, CWI Quarterly 4:1 (1991), 3--26.
Multiparameter Quantum Supergroups - Hazewinkel Self-citation (Hazewinkel) (Correct)
.... matrix function algebra comultiplication t i j 7 t i k Omega t k j (1.3) where the Einstein summation convention is in force, i.e. on the righthand side of (1.3) a sum over k is implied. This makes K t a bialgebra and it is always the case that I(R) is a bialgebra ideal; cf e.g. [4] for a proof. Thus Kn (R) K t =I(R) 1.4) inherits a bialgebra structure. This is sometimes called the FRT construction (Faddeev Reshetikin Taktadzhyan) It was also indepedently noticed by other authors. Relations like (1.1) first came up in the work of the Faddeev group in what was ....
Michiel Hazewinkel, Introductory recommendations for the study of Hopf algebras in mathematics and physics, CWI Quarterly 4:1 (1991), 3--26.
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