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Value functions on simple algebras, and associated graded rings

This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's...

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Detalles Bibliográficos
Autores principales: Tignol, Jean-Pierre, Wadsworth, Adrian R
Lenguaje:eng
Publicado: Springer 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-16360-4
http://cds.cern.ch/record/2015363
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author Tignol, Jean-Pierre
Wadsworth, Adrian R
author_facet Tignol, Jean-Pierre
Wadsworth, Adrian R
author_sort Tignol, Jean-Pierre
collection CERN
description This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of noncrossed products and Platonov's solution of the Tannaka-Artin problem. This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased. The intended audience consists of graduate students and research mathematicians.
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spelling cern-20153632021-04-21T20:19:10Zdoi:10.1007/978-3-319-16360-4http://cds.cern.ch/record/2015363engTignol, Jean-PierreWadsworth, Adrian RValue functions on simple algebras, and associated graded ringsMathematical Physics and MathematicsThis monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of noncrossed products and Platonov's solution of the Tannaka-Artin problem. This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased. The intended audience consists of graduate students and research mathematicians.Springeroai:cds.cern.ch:20153632015
spellingShingle Mathematical Physics and Mathematics
Tignol, Jean-Pierre
Wadsworth, Adrian R
Value functions on simple algebras, and associated graded rings
title Value functions on simple algebras, and associated graded rings
title_full Value functions on simple algebras, and associated graded rings
title_fullStr Value functions on simple algebras, and associated graded rings
title_full_unstemmed Value functions on simple algebras, and associated graded rings
title_short Value functions on simple algebras, and associated graded rings
title_sort value functions on simple algebras, and associated graded rings
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-16360-4
http://cds.cern.ch/record/2015363
work_keys_str_mv AT tignoljeanpierre valuefunctionsonsimplealgebrasandassociatedgradedrings
AT wadsworthadrianr valuefunctionsonsimplealgebrasandassociatedgradedrings