Xambó-Descamps, Sebastià
Real spinorial groups : a short mathematical introduction [Documento electrónico] / Sebastià Xambó-Descamps. - Cham : Springer International Publishing : Springer , 2018 . - X, 151 p. : il.. - (SpringerBriefs in Mathematics) This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-030-00404-0
Geometria
Teoria dos grupos
Física matemática
LCC QA443
Real spinorial groups : a short mathematical introduction [Documento electrónico] / Sebastià Xambó-Descamps. - Cham : Springer International Publishing : Springer , 2018 . - X, 151 p. : il.. - (SpringerBriefs in Mathematics) This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-030-00404-0
Geometria
Teoria dos grupos
Física matemática
LCC QA443
