Amnon Yekutieli's Books

Derived Categories

By: Amnon Yekutieli

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There have been remarkably few systematic expositions of the theory of derived categories since its inception in the work of Grothendieck and Verdier in the 1960s. This book is the first in-depth treatment of this important component of homological algebra. It carefully explains the foundations in detail before moving on to key applications in commutative and noncommutative algebra, many otherwise unavailable outside of research articles. These include commutative and noncommutative dualizing complexes, perfect DG modules, and tilting DG bimodules. Written with graduate students in mind, the emphasis here is on explicit constructions (with many examples and exercises) as opposed to axiomatics, with the goal of demystifying this difficult subject. Beyond serving as a thorough introduction for students, it will serve as an important reference for researchers in algebra, geometry and mathematical physics.

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Page Count

622

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Cambridge University Press

Published Date

ISBN 10

1108321607

ISBN 13

9781108321600

Derived Categories

By: Amnon Yekutieli

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Derived Categories

By: Amnon Yekutieli

The first systematic exposition of the theory of derived categories, with key applications in commutative and noncommutative algebra.

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621

Publisher

Cambridge University Press

Published Date

ISBN 10

110841933X

ISBN 13

9781108419338

Nonabelian Multiplicative Integration On Surfaces

By: Amnon Yekutieli

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Nonabelian Multiplicative Integration On Surfaces

By: Amnon Yekutieli

Nonabelian multiplicative integration on curves is a classical theory. This volume is about the 2-dimensional case, which is much more difficult. In our construction, the setup is a Lie crossed module: there is a Lie group H, together with an action on it by another Lie group G. The multiplicative integral is an element of H, and it is the limit of Riemann products. Each Riemann product involves a fractal decomposition of the surface into kites (triangles with strings connecting them to the base point). There is a twisting of the integrand, that comes from a 1-dimensional multiplicative integral along the strings, with values in the group G.The main result of this work is the 3-dimensional nonabelian Stokes theorem. This result is new; only a special case of it was predicted (without proof) in papers in mathematical physics. Our constructions and proofs are of a straightforward nature. There are plenty of illustrations to clarify the geometric constructions.Our volume touches on some of the central issues (e.g., descent for nonabelian gerbes) in an unusually down-to-earth manner, involving analysis, differential geometry, combinatorics and Lie theory — instead of the 2-categories and 2-functors that other authors prefer.

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Page Count

186

Publisher

World Scientific

Published Date

ISBN 10

9814663867

ISBN 13

9789814663861

Nonabelian Multiplicative Integration On Surfaces

By: Amnon Yekutieli

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Nonabelian Multiplicative Integration On Surfaces

By: Amnon Yekutieli

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Page Count

186

Publisher

World Scientific

Published Date

ISBN 10

9814663867

ISBN 13

9789814663861

Book's by Amnon Yekutieli

Derived Categories

Derived Categories

Derived Categories

Derived Categories

Nonabelian Multiplicative Integration On Surfaces

Nonabelian Multiplicative Integration On Surfaces

Nonabelian Multiplicative Integration On Surfaces

Nonabelian Multiplicative Integration On Surfaces

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