Автор: Wood Название: The Twisted Cubic ISBN: 1107493722 ISBN-13(EAN): 9781107493728 Издательство: Cambridge Academ Рейтинг: Цена: 3008.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Originally published in 1913 as number fourteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the properties of the twisted cubic. A bibliography and appendix section are also included.
Автор: Henderson Название: The Twenty-Seven Lines upon the Cubic Surface ISBN: 110749351X ISBN-13(EAN): 9781107493513 Издательство: Cambridge Academ Рейтинг: Цена: 3643.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Originally published in 1911 as number thirteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book presents a general survey of the problem of the 27 lines upon the cubic surface. Illustrative figures and a bibliography are also included.
Автор: Hambleton Samuel A., Williams Hugh C. Название: Cubic Fields with Geometry ISBN: 3030014029 ISBN-13(EAN): 9783030014025 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The objective of this book is to provide tools for solving problems which involve cubic number fields. Many such problems can be considered geometrically; both in terms of the geometry of numbers and geometry of the associated cubic Diophantine equations that are similar in many ways to the Pell equation. With over 50 geometric diagrams, this book includes illustrations of many of these topics. The book may be thought of as a companion reference for those students of algebraic number theory who wish to find more examples, a collection of recent research results on cubic fields, an easy-to-understand source for learning about Voronoi’s unit algorithm and several classical results which are still relevant to the field, and a book which helps bridge a gap in understanding connections between algebraic geometry and number theory.
The exposition includes numerous discussions on calculating with cubic fields including simple continued fractions of cubic irrational numbers, arithmetic using integer matrices, ideal class group computations, lattices over cubic fields, construction of cubic fields with a given discriminant, the search for elements of norm 1 of a cubic field with rational parametrization, and Voronoi's algorithm for finding a system of fundamental units. Throughout, the discussions are framed in terms of a binary cubic form that may be used to describe a given cubic field. This unifies the chapters of this book despite the diversity of their number theoretic topics.
Автор: Matthias Gruninger Название: Cubic Action of a Rank One Group ISBN: 1470451344 ISBN-13(EAN): 9781470451349 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 10659.00 р. Наличие на складе: Поставка под заказ.
Описание: We consider a rank one group G = A,Bacting cubically on a module V, this means [V,A,A,A] = 0 but [V,G,G,G]= 0. We have to distinguish whether the group A0 := CA([V,A]) ?CA(V/CV(A)) is trivial or not. We show that if A0 is trivial, G is a rank one group associated toa quadratic Jordan division algebra. If A0 is not trivial (which is always the case if A is not abelian), then A0 defines a subgroup G0 of G acting quadratically on V . We will call G0 the quadratic kernel of G. By a result of Timmesfeld we have G0 ?= SL2(J,R) for a ring R and a special quadratic Jordan division algebra J ? R. We show that J is either a Jordan algebra contained in a commutative field or a Hermitian Jordan algebra. In the second case G is the special unitary group of a pseudo-quadratic form ? of Witt index 1, in the first case G is the rank one group for a Freudenthal triple system. These results imply that if (V,G) is a quadratic pair such that no two distinct root groups commute and charV=2,3, then G is a unitary group or an exceptional algebraic group.
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