2015
DOI: 10.1007/978-3-319-18991-8
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Fundamentals of Hopf Algebras

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Cited by 40 publications
(8 citation statements)
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References 25 publications
(32 reference statements)
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“…KG is an algebra with multiplication given by µ(g ⊗ h) = gh and a unit map given by λ(r) = r1 for all g, h ∈ G and r ∈ K [25]. KG is a coalgebra with comultiplication given by ∆(g) = g ⊗ g and a counit map given by (g) = 1 for all g ∈ G. Moreover, KG is a Hopf algebra with an antipode map given by S(g) = g −1 for all g ∈ G [9].…”
Section: The Group Algebra H = Rcmentioning
confidence: 99%
“…KG is an algebra with multiplication given by µ(g ⊗ h) = gh and a unit map given by λ(r) = r1 for all g, h ∈ G and r ∈ K [25]. KG is a coalgebra with comultiplication given by ∆(g) = g ⊗ g and a counit map given by (g) = 1 for all g ∈ G. Moreover, KG is a Hopf algebra with an antipode map given by S(g) = g −1 for all g ∈ G [9].…”
Section: The Group Algebra H = Rcmentioning
confidence: 99%
“…Algebras and tensors. In general algebra [24,23], a bialgebra in some vector space V over some field K is something that satifies all axioms of Definition 3 when arrows from n → m are linear maps from V ⊗n to V ⊗m .…”
Section: Consequences and Applicationsmentioning
confidence: 99%
“…These are the first examples in[24] and the first commutative examples in[23]. In[23] the binomial algebra is seen as a bialgebra over the symmetric algebra 6.…”
mentioning
confidence: 99%
“…Since the algebra C[X] is a principal ideal domain, it turns out that the space of linearly recursive sequences Lin(C) can be identified with C[X] • via the isomorphism Φ, whence it becomes an augmented subalgebra of HC N and a Hopf algebra. For further reading, we refer the interested reader to [3,6,10] and [11,Chapter 2].…”
Section: The Space Of Linearly Recursive Sequences and Hurwitz's Productmentioning
confidence: 99%