Tangent Coalgebras and Hyperalgebras I
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This article is published in Japanese journal of mathematics :transactions and abstracts.The article was published on 1974-01-01 and is currently open access. It has received 29 citations till now. The article focuses on the topics: Tangent.read more
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Cohomology, hyperalgebras, and representations
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Harish-Chandra pairs for algebraic affine supergroup schemes over an arbitrary field
TL;DR: In this article, the notion of Harish-Chandra pairs was defined and proved to be anti-equivalent to the category of algebraic affine supergroup schemes over an arbitrary field of characteristic ≠ 2.
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Support varieties for algebraic groups
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The fundamental correspondences in super affine groups and super formal groups
TL;DR: Some basic results on super affine groups and super formal groups in arbitrary characteristic ( ≠ 2 ) are proved in terms of super Hopf algebras, including the fundamental correspondence between subgroups and quotients.
References
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Cohomology of algebras over Hopf algebras
TL;DR: In this paper, it was shown that the natural transformation from the Amitsur cohomology of A to H*(H, A) is an isomorphism, which implies that A is a finite field extension.
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Reflexivity and coalgebras of finite type
TL;DR: In this article, the authors studied various finiteness conditions on a coalgebra C and the dual algebra C* of all linear functionals on C. They showed that C is a rational coalgebra if every finite function on C* is induced by an element of C. And they showed that any connected coalgebra may be imbedded in the shuffle coalgebra Sh(F) (where si is the space of primitive elements of C).
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Hopf algebras with one grouplike element
TL;DR: The coalgebra structure of cocommutative Hopf algebras was studied in this article, where it was shown that the primitive sub-Hopf algebra of a cocomutative hopf algebra with antipode can be primitively generated over an algebraically closed field, provided the characteristic of the field is not zero.