Nichols Algebras of Unidentified Diagonal Type
نویسندگان
چکیده
منابع مشابه
Lusztig Isomorphisms for Drinfel’d Doubles of Bosonizations of Nichols Algebras of Diagonal Type
In the structure theory of quantized enveloping algebras, the algebra isomorphisms determined by Lusztig led to the first general construction of PBW bases of these algebras. Also, they have important applications to the representation theory of these and related algebras. In the present paper the Drinfel’d double for a class of graded Hopf algebras is investigated. Various quantum algebras, in...
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The paper introduces a new method to determine all rank two Nichols algebras of diagonal type over fields of positive characteristic.
متن کاملLusztig Isomorphisms for Drinfel’d Doubles of Nichols Algebras of Diagonal Type
In the structure theory of quantized enveloping algebras, the algebra isomorphisms determined by Lusztig led to the first general construction of PBW bases of these algebras. Also, they have important applications to the representation theory of these and related algebras. In the present paper the Drinfel’d double for a class of graded Hopf algebras is investigated. Various quantum algebras, in...
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Nichols algebras naturally appear in the classification of finite dimensional pointed Hopf algebras. Assuming only that the base field has characteristic zero several new finite dimensional rank 2 Nichols algebras of diagonal type are listed. Each of them is described in terms of generators and relations. A Poincaré–Birkhoff–Witt basis of all of these Nichols algebras is given and their dimensi...
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We compute liftings of the Nichols algebra of a Yetter-Drinfeld module of Cartan type B2 subject to the small restriction that the diagonal elements of the braiding matrix are primitive nth roots of 1 with odd n 6= 5. As well, we compute the liftings of a Nichols algebra of Cartan type A2 if the diagonal elements of the braiding matrix are cube roots of 1; this case was not completely covered i...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2013
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2012.700980