Bicharacters, Twistings, and Scheunert's Theorem for Hopf Algebras

Bahturin, Yuri; Fischman, Davida; Montgomery, Susan

doi:10.1006/jabr.2000.8520

Cited by 30 publications

(32 citation statements)

References 23 publications

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“…The equivalent conditions for S 2 = id H for H co-Frobenius may remind the reader of analogous conditions in the quasi-triangular and coquasi-triangular case. It is a well-known theorem of Drinfel'd [6] (also proved by Radford [23]) that for (H, R = R (1) ⊗ R (2) ) quasitriangular, then S 2 is an inner automorphism of H , i.e., S 2 (h) = uhu −1 where u = S(R (2) )R (1) .…”

Section: Integrals and The Square Of The Antipodementioning

confidence: 99%

Radford's S4 formula for co-Frobenius Hopf algebras

2007

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Section: Integrals and The Square Of The Antipodementioning

confidence: 99%

Radford's S4 formula for co-Frobenius Hopf algebras

2007

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“…where |v| denotes the degree of v. In this case a (H, R)-lie algebra (V, [−, −]) in the sense of [BFM,Definition 4.1] means…”

Section: Examples Of Mm-categoriesmentioning

confidence: 99%

Milnor–Moore categories and monadic decomposition

Ardizzoni

Menini

2016

Journal of Algebra

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Abstract. In this paper Hom-Lie algebras, Lie color algebras, Lie superalgebras and other type of generalized Lie algebras are recovered by means of an iterated construction, known as monadic decomposition of functors, which is based on Eilenberg-Moore categories. To this aim we introduce the notion of Milnor-Moore category as a monoidal category for which a MilnorMoore type Theorem holds. We also show how to lift the property of being a Milnor-Moore category whenever a suitable monoidal functor is given and we apply this technique to provide examples.

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“…In this case, it is a well known theorem of Scheunert [14] that θ arises from a 2-cocycle (as mentioned in the previous remark). The notion of a bicharacter was considerably generalized to cocommutative Hopf algebras (and hence in particular to group algebras) (see [4]). Furthermore, whenever the bicharacter is skew symmetric, the theorem of Scheunert can be extended to that case.…”

Section: Theorem 12 Theorem 7(1) Holds For Arbitrary Nondegenerate Rmentioning

confidence: 99%

On regular 𝐺-gradings

Aljadeff¹,

David²

2014

Trans. Amer. Math. Soc.

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Let A be an associative algebra over an algebraically closed field F of characteristic zero and let G be a finite abelian group. Regev and Seeman introduced the notion of a regular Ggrading on A, namely a grading A = g∈G Ag that satisfies the following two conditions: (1) for every integer n ≥ 1 and every n-tuple (g1, g2, . . . , gn) ∈ G n , there are elements, ai ∈ Ag i , i = 1, . . . , n, such that n 1 ai = 0 (2) for every g, h ∈ G and for every ag ∈ Ag, b h ∈ A h , we have agb h = θ g,h b h ag. Then later, Bahturin and Regev conjectured that if the grading on A is regular and minimal, then the order of the group G is an invariant of the algebra. In this article we prove the conjecture by showing that ord(G) coincides with an invariant of A which appears in PI theory, namely exp(A) (the exponent of A). Moreover, we extend the whole theory to (finite) nonabelian groups and show that the above result holds also in that case.

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Bicharacters, Twistings, and Scheunert's Theorem for Hopf Algebras

Cited by 30 publications

References 23 publications

Radford's S4 formula for co-Frobenius Hopf algebras

Radford's S4 formula for co-Frobenius Hopf algebras

Milnor–Moore categories and monadic decomposition

On regular 𝐺-gradings

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