Results 1 to 10 of about 85 (85)
Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type
Advances in Mathematical Physics, 2021 Nichols algebras are fundamental objects in the construction of quantized enveloping algebras and in the classification of pointed Hopf algebras by the lifting method of Andruskiewitsch and Schneider. The structure of Cartan graphs can be attached to any
Chen Qian, Jing Wang
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EXAMPLES OF POINTED COLOR HOPF ALGEBRAS [PDF]
Journal of Algebra and Its Applications, 2013 We present examples of color Hopf algebras, i.e. Hopf algebras in color categories (braided tensor categories with braiding induced by a bicharacter on an abelian group), related with quantum doubles of pointed Hopf algebras. We also discuss semisimple color Hopf algebras.
Andruskiewitsch, Nicolás +2 more
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CLASSIFICATION OF QUIVER HOPF ALGEBRAS AND POINTED HOPF ALGEBRAS OF TYPE ONE [PDF]
Bulletin of the Australian Mathematical Society, 2012 AbstractQuiver Hopf algebras are classified by means of ramification systems with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one.
Zhang, Shouchuan +2 more
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Cohomology of finite-dimensional pointed Hopf algebras [PDF]
Proceedings of the London Mathematical Society, 2009 36 pages, references ...
Mastnak, M. +3 more
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POINTED HOPF ALGEBRAS WITH CLASSICAL WEYL GROUPS [PDF]
International Journal of Mathematics, 2012 We prove that Nichols algebras of irreducible Yetter–Drinfeld modules over classical Weyl groups A ⋊ 𝕊nsupported by 𝕊nare infinite dimensional, except in three cases. We give necessary and sufficient conditions for Nichols algebras of Yetter–Drinfeld modules over classical Weyl groups A ⋊ 𝕊nsupported by A to be finite dimensional.
Zhang, Shouchuan, Zhang, Yao-Zhong
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On finite dimensional Nichols algebras of diagonal type
Bulletin of Mathematical Sciences, 2017 This is a survey on Nichols algebras of diagonal type with finite dimension, or more generally with arithmetic root system. The knowledge of these algebras is the cornerstone of the classification program of pointed Hopf algebras with finite dimension ...
Nicolás Andruskiewitsch, Iván Angiono
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Pointed Hopf Algebras and Quasi-isomorphisms [PDF]
Algebras and Representation Theory, 2005 19 pages, added section with new result, rest mainly ...
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Pointed Hopf Algebras of Dimensionp3
Journal of Algebra, 1998 The authors prove that, over an algebraically closed field \(k\) of characteristic 0, if \(H\) is a Hopf algebra with coradical \(kC_p\), \(p\) prime, then the dimension of \(H_1\) is \(3p\). Thus \(H\) is generated by \(c\), a grouplike element of order \(p\), together with skew-primitives \(x\) and \(y\) with \(x^p=y^p=0\) and either \(yx=\lambda xy\)
Caenepeel, Stefaan, Dascalescu, S.
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, 2001 This is a survey on pointed Hopf algebras over algebraically closed fields of characteristic 0. We propose to classify pointed Hopf algebras $A$ by first determining the graded Hopf algebra $\gr A$ associated to the coradical filtration of $A$. The $A_{0}$-coinvariants elements form a braided Hopf algebra $R$ in the category of Yetter-Drinfeld modules ...
Andruskiewitsch, N., Schneider, H. -J.
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Coverings of graded pointed Hopf algebras
Journal of Algebra, 2015 We introduce the concept of a covering of a graded pointed Hopf algebra. The theory developed shows that coverings of a bosonized Nichols algebra can be concretely expressed by biproducts using a quotient of the universal coalgebra covering group of the Nichols algebra.
Beneish, Esther, Chin, William
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