Results 11 to 20 of about 2,471 (100)
On defining ideals and differential algebras of Nichols algebras
Journal of Algebra, 2011 This paper is devoted to understanding the defining ideal of a Nichols algebra from the decomposition of specific elements in the group algebra of braid groups. A family of primitive elements are found and algorithms are proposed. To prove the main result, the differential algebra of a Nichols algebra is constructed.
Xin Fang
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Nichols Algebras and Quantum Principal Bundles
International Mathematics Research Notices, 2018 A general procedure for constructing Yetter-Drinfeld modules from quantum principal bundles is introduced. As an application a Yetter-Drinfeld structure is put on the cotangent space of the Heckenberger-Kolb calculi of the quantum Grassmannians.
Buachalla, Réamonn Ó
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A Freeness Theorem for Nichols Algebras
Journal of Algebra, 2000 For \(V\) a vector space and \((V,c)\) a rigid solution of the braid equation, then the quantum symmetric algebra (QSA or \({\mathcal B}(V)\)) constructed from the tensor algebra \(AV\) and the tensor coalgebra \(CV\) is called a Nichols algebra. A Nichols algebra is a braided Hopf algebra in a rigid braided category.
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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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Lie Algebras Arising from Nichols Algebras of Diagonal Type [PDF]
International Mathematics Research Notices, 2021 AbstractLet $\mathcal{B}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type with braiding matrix $\mathfrak{q}$, $\mathcal{L}_{\mathfrak{q}}$ be the corresponding Lusztig algebra as in [ 4], and $\operatorname{Fr}_{\mathfrak{q}}: \mathcal{L}_{\mathfrak{q}} \to U(\mathfrak{n}^{\mathfrak{q}})$ be the corresponding quantum Frobenius ...
Andruskiewitsch, Nicolás +2 more
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THE NICHOLS ALGEBRA OF SCREENINGS [PDF]
Communications in Contemporary Mathematics, 2012 Two related constructions are associated with screening operators in models of two-dimensional conformal field theory. One is a local system constructed in terms of the braided vector space X spanned by the screening species in a given CFT model and the space of vertex operators Y and the other is the Nichols algebra 𝔅(X) and the category of its Yetter–
Semikhatov, A. M., Tipunin, I. Yu.
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On Nichols algebras over basic Hopf algebras [PDF]
Mathematische Zeitschrift, 2020 This is a contribution to the classification of finite-dimensional Hopf algebras over an algebraically closed field $\Bbbk$ of characteristic 0. Concretely, we show that a finite-dimensional Hopf algebra whose Hopf coradical is basic is a lifting of a Nichols algebra of a semisimple Yetter-Drinfeld module and we explain how to classify Nichols algebras
Andruskiewitsch, Nicolas +1 more
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Nichols algebras with many cubic relations [PDF]
Transactions of the American Mathematical Society, 2015 46 pages, 20 figures. We improved significantly the text by adding more definitions and more explanations.
Heckenberger, I. +2 more
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Nichols algebras over classical Weyl groups(II) [PDF]
International Journal of Mathematics, 2021 It is shown that except in three cases conjugacy classes of classical Weyl groups [Formula: see text] and [Formula: see text] are of type [Formula: see text]. This proves that Nichols algebras of irreducible Yetter–Drinfeld modules over the classical Weyl groups [Formula: see text] (i.e.
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Algebras of Non-Local Screenings and Diagonal Nichols Algebras
Symmetry, Integrability and Geometry: Methods and Applications, 2022 In a vertex algebra setting, we consider non-local screening operators associated to the basis of any non-integral lattice. We have previously shown that, under certain restrictions, these screening operators satisfy the relations of a quantum shuffle algebra or Nichols algebra associated to a diagonal braiding, which encodes the non-locality and non ...
Flandoli, Ilaria, Lentner, Simon D.
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