Hopf Algebras in Noncommutative Geometry and Physics by Stefaan Caenepeel

By Stefaan Caenepeel

This complete reference summarizes the lawsuits and keynote shows from a contemporary convention held in Brussels, Belgium. supplying 1155 show equations, this quantity comprises unique examine and survey papers in addition to contributions from world-renowned algebraists. It makes a speciality of new ends up in classical Hopf algebras in addition to the class concept of finite dimensional Hopf algebras, specific features of Hopf algebras, and up to date advances within the concept of corings and quasi-Hopf algebras. It presents examples and simple houses of corings and their comodules relating to ring and Hopf algebra conception and analyzes entwining buildings and Morita thought for corings.

Show description

Read or Download Hopf Algebras in Noncommutative Geometry and Physics PDF

Best linear books

A first course in linear algebra

A primary direction in Linear Algebra is an creation to the fundamental strategies of linear algebra, besides an creation to the recommendations of formal arithmetic. It starts with structures of equations and matrix algebra ahead of entering into the idea of summary vector areas, eigenvalues, linear ameliorations and matrix representations.

Measure theory/ 3, Measure algebras

Fremlin D. H. degree conception, vol. three (2002)(ISBN 0953812936)(672s)-o

Elliptic Partial Differential Equations

Elliptic partial differential equations is among the major and so much energetic parts in arithmetic. In our ebook we research linear and nonlinear elliptic difficulties in divergence shape, with the purpose of delivering classical effects, in addition to more moderen advancements approximately distributional strategies. for that reason the ebook is addressed to master's scholars, PhD scholars and someone who desires to start examine during this mathematical box.

Additional info for Hopf Algebras in Noncommutative Geometry and Physics

Example text

Is Assume that a C is locally projective, bA is flat and A /B is C-Galois. e. cr[A*c] = (^[C*c]i injective, for every M G ; an isomorphism, for every A-generated M G . Proof 1. Since A /B is C-Galois, is an isomorphism, hence C is Agenerated. Consequently cr[A*c] ^ £ ^[-^*c]j he. cf[A*c] = cr[C*c]2 . 22] applies. 3. U M £ MP is A-generated, then is surjective, hence bijective by ( 2). 13] (which is itself a generalization of [14, Theorem 2 . 11]). 2. Assume that A /B is C-Galois. 1. If b A is flat, then satisfies the weak structure theorem.

A, A ^ A(M) and Ti. + {n~'^)u + Dv + Duv \{M ) = A(M). 5. i-order. If F is a maximal D-order then it is also an W-order and thus a maximal W-order. Proof. Since L is an 7i-lattice, A(L) is an W-order and since L is a left ideal for F, we have F C A(L). The other statement is obvious from this. 3, we may obtain a first char­ acterization of maximal W-orders in terms of maximal orders. If A is a maximal H-order in A, then there is a maximal order F in A such that A = \{ H —^ F) = p{H —^ F). 6. Proof.

J. 30 (1981), 675-692. [19] C. Menini, A. Seidel, B. Torrecillas and R. Wisbauer, A-if-bimodules and equivalences. Comm. Algebra 29 (2001), 4619-4640. [20] C. Menini, B. Torrecillas and R. Wisbauer, Strongly rational comodules and semiperfect Hopf algebras over QF Rings, J. Pure Appl. Algebra 155 (2001), 237-255. [21] C. Menini and M. Zuccoli, Equivalence Theorems and Hopf-Galois extensions, J. Algebra 194 (1997), 245-274. [22] H. J. Schneider, Principal homogeneous spaces for arbitrary Hopf algebras, Israel J.

Download PDF sample

Rated 4.53 of 5 – based on 41 votes