The Picard group of a structural matrix algebra
نویسندگان
چکیده
منابع مشابه
The Picard group
Why should a number theorist be interested in algebraic geometry? In this course we hope to demonstrate one very good reason, by showing essentially geometric reasons why certain Diophantine equations fail to have solutions. But we will begin by placing the study of Diophantine equations into the context of algebraic geometry, to see how techniques from many different realms of mathematics can ...
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Let A be a commutative comodule algebra over a commutative bialgebra H . The group of invertible relative Hopf modules maps to the Picard group of A, and the kernel is described as a quotient group of the group of invertible grouplike elements of the coring A⊗H , or as a Harrison cohomology group. Our methods are based on elementary K-theory. The Hilbert 90 Theorem follows as a corollary. The p...
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The loop space LP1 of the Riemann sphere consisting of all C k or Sobolev W k,p maps S → P1 is an infinite dimensional complex manifold. We compute the Picard group Pic(LP1) of holomorphic line bundles on LP1 as an infinite dimensional complex Lie group with Lie algebra the Dolbeault group H(LP1). The group of Möbius transformations G and its loop group LG act on LP1. We prove that an element o...
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In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the convolution measure algebra M, (S) of a locally compact semigroup. H. Dzinotyiweyi in [5,7] considers an analogous measure space on a large class of C-distinguished topological semigroups containing all completely regular topological semigroups. In this paper, we extend the definitions to study the weighted semigroup ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2000
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00200-1