Formal groups and Hopf algebras over discrete rings
نویسندگان
چکیده
منابع مشابه
Formal groups over Hopf algebras
The aim of this section is to define some generalization of the notion of formal group. More precisely, we consider the analog of formal groups with coefficients belonging to a Hopf algebra. We also study some example of a formal group over a Hopf algebra, which generalizes the formal group of geometric cobordisms. Recently some important connections between the Landweber-Novikov algebra and th...
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In this note we develop a theory of formal schemes and groups over arbitrary commutative rings which coincides with that of [5] if the base ring is a field, and generalizes that of [2]. We assume always our base ring is discrete and treat a formal scheme (resp. group) G, with two principal tools: A topology on the affine algebra (9(G) allows us to form its continuous linear dual B(G), the coalg...
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This paper is the continuation of section 2 of the paper ”Floating bundles and their applications” [1]. Let (H, μ, η,∆, ε, S) be a commutative Hopf algebra over ring R without torsion and F(x ⊗ 1, 1⊗ x) be a formal group over Hopf algebra H. By HQ denote the Hopf algebra H⊗ Z Q over ring RQ = R⊗ Z Q. We shall write μ, η, . . . instead of μQ, ηQ, . . . . The aim of this paper is to prove the fol...
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Integrals in Hopf algebras are an essential tool in studying finite dimensional Hopf algebras and their action on rings. Over fields it has been shown by Sweedler that the existence of integrals in a Hopf algebra is equivalent to the Hopf algebra being finite dimensional. In this paper we examine how much of this is true for Hopf algebras over rings. We show that over any commutative ring R tha...
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The class of finite-dimensional pointed Hopf algebras is a field of current active research. The classification of these algebras has seen substantial progress since the development of the so-called “Lifting method” by Andruskiewitsch and Schneider. With this tool, the case in which the group of group-like elements is abelian is almost completed and recent results by these and other authors suc...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1974-0366935-2