Results 161 to 170 of about 600 (187)
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Canadian Journal of Mathematics, 1967
A coalgebra over the field F is a vector space A over F, with maps δ: A → A ⊗ A and ∊: A → F such that1and2The notion of coalgebra is dual to the notion of algebra with unit, with δ as coproduct (equation (1) says that δ is associative) and ∊ as the unit map (equation (2) is just the statement that ∊ is a unit for the coproduct δ).
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A coalgebra over the field F is a vector space A over F, with maps δ: A → A ⊗ A and ∊: A → F such that1and2The notion of coalgebra is dual to the notion of algebra with unit, with δ as coproduct (equation (1) says that δ is associative) and ∊ as the unit map (equation (2) is just the statement that ∊ is a unit for the coproduct δ).
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American Journal of Mathematics, 1977
Let A be a finite dimensional Hopf algebra with antipode s over a field k. In (6) the structure of s and s2 is seen to be closely related to the important algebraic features of A and A*. This paper furthers the investigation. More generally "locally finite" bialgebra endomorphisms t:A ->A of an arbitrary Hopf algebra A are considered (this means A is ...
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Let A be a finite dimensional Hopf algebra with antipode s over a field k. In (6) the structure of s and s2 is seen to be closely related to the important algebraic features of A and A*. This paper furthers the investigation. More generally "locally finite" bialgebra endomorphisms t:A ->A of an arbitrary Hopf algebra A are considered (this means A is ...
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Journal of the London Mathematical Society, 1991
This paper deals with graded Hopf algebras of the kind represented by the homology of the loops on simply connected spaces of finite type or universal enveloping algebras of graded Lie algebras of finite type (i.e. degree-wise finite-dimensional). In particular, finitely generated nilpotent (elliptic) Hopf algebras are characterized in several ways: by
Félix, Yves +2 more
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This paper deals with graded Hopf algebras of the kind represented by the homology of the loops on simply connected spaces of finite type or universal enveloping algebras of graded Lie algebras of finite type (i.e. degree-wise finite-dimensional). In particular, finitely generated nilpotent (elliptic) Hopf algebras are characterized in several ways: by
Félix, Yves +2 more
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Nonlinear Evolution Equations and Dynamical Systems, 2003
Abstract: This lecture was given in UIA at Antwerp, and in USTC at Hefei, aiming at outlining a construction of non-commutative, non-cocommutative pointed Hopf algebras via quivers, given by Cibils and Rosso(3). We thank Sen Hu for his interest to include it in this proceeding. To save the space, we omit details here.
Van Oystaeyen, F., Zhang, P.
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Abstract: This lecture was given in UIA at Antwerp, and in USTC at Hefei, aiming at outlining a construction of non-commutative, non-cocommutative pointed Hopf algebras via quivers, given by Cibils and Rosso(3). We thank Sen Hu for his interest to include it in this proceeding. To save the space, we omit details here.
Van Oystaeyen, F., Zhang, P.
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International Journal of Theoretical Physics, 2001
This is a short survey article on the Hopf algebra \(H^0\), the continuous Hopf algebra dual of the complex polynomial Hopf algebra \(H=\mathbb{C}[x]\) in one primitive variable \(x\). Various realizations of \(H^0\) are given. One is the complex vector space spanned by the rational functions \({1\over(z-a)^{k+1}}\), for \(a\) in \(\mathbb{C}\), \(k ...
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This is a short survey article on the Hopf algebra \(H^0\), the continuous Hopf algebra dual of the complex polynomial Hopf algebra \(H=\mathbb{C}[x]\) in one primitive variable \(x\). Various realizations of \(H^0\) are given. One is the complex vector space spanned by the rational functions \({1\over(z-a)^{k+1}}\), for \(a\) in \(\mathbb{C}\), \(k ...
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On some classification of finite-dimensional Hopf algebras over the Hopf algebra Hb:1* of Kashina
Communications in Algebra, 2023Yuxing Shi
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A GL(Fq)-compatible Hopf algebra of unitriangular class functions
Journal of Algebra, 2023Lucas Gagnon
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Gorenstein subrings of invariants under Hopf algebra actions
Journal of Algebra, 2009J J Zhang, E Kirkman
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