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This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type $F_4$ or $G_2$ arising from exceptional Jordan or composition algebras. Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type $D_4$. This volume also contains a Bibliography and Index. Features: original material not in print elsewhere a comprehensive discussion of algebra-theoretic and group-theoretic aspects extensive notes that give historical perspective and a survey on the literature rational methods that allow possible generalization to more general base rings

Author : Max-Albert Knus
ISBN : 9780821809044
Genre : Mathematics
File Size : 48.48 MB
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Written for graduate students and research mathematicians, this monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. Involutions are viewed as twisted forms of hermitian quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are discussed, as well as: groups of type F4 or G2 arising from exceptional Jordan or composition algebras, the discriminant algebra of an algebra with unitary involution, and the algebra-theoretic counterpart to linear groups of type D4. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Max-Albert Knus
ISBN : 9780821809044
Genre : Mathematics
File Size : 59.15 MB
Format : PDF
Download : 579
Read : 1317

Written for graduate students and research mathematicians, this monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. Involutions are viewed as twisted forms of hermitian quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are discussed, as well as: groups of type F4 or G2 arising from exceptional Jordan or composition algebras, the discriminant algebra of an algebra with unitary involution, and the algebra-theoretic counterpart to linear groups of type D4. Annotation copyrighted by Book News, Inc., Portland, OR.

Written for graduate students and research mathematicians, this monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. Involutions are viewed as twisted forms of hermitian quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are discussed, as well as: groups of type F4 or G2 arising from exceptional Jordan or composition algebras, the discriminant algebra of an algebra with unitary involution, and the algebra-theoretic counterpart to linear groups of type D4. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Werner M. Seiler
ISBN : 9783642012877
Genre : Mathematics
File Size : 84.40 MB
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The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.

Author : Mark Pankov
ISBN : 9789814317566
Genre : Mathematics
File Size : 60.15 MB
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Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains both classical and more recent results on Grassmannians of buildings of classical types. It gives a modern interpretation of some classical results from the geometry of linear groups. The presented methods are applied to some geometric constructions non-related to buildings Grassmannians of infinite-dimensional vector spaces and the sets of conjugate linear involutions. The book is self-contained and the requirement for the reader is a knowledge of basic algebra and graph theory. This makes it very suitable for use in a course for graduate students.

Author : Alberto Cabada
ISBN : 9789462391215
Genre : Mathematics
File Size : 57.70 MB
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This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.

This volume is concerned with algebraic invariants, such as the Stiefel-Whitney classes of quadratic forms (with values in Galois cohomology mod 2) and the trace form of etale algebras (with values in the Witt ring). The invariants are analogues for Galois cohomology of the characteristic classes of topology. Historically, one of the first examples of cohomological invariants of the type considered here was the Hasse-Witt invariant of quadratic forms. The first part classifies such invariants in several cases. A principal tool is the notion of versal torsor, which is an analogue of the universal bundle in topology. The second part gives Rost's determination of the invariants of $G$-torsors with values in $H^3(\mathbb{Q}/\mathbb{Z}(2))$, when $G$ is a semisimple, simply connected, linear group. This part gives detailed proofs of the existence and basic properties of the Rost invariant. This is the first time that most of this material appears in print.

Winner of the MLA Prize for Independent Scholars Taking the reader on an inward journey from façades to closets, from physical to psychic space, Architectural Involutions offers an alternative genealogy of theater by revealing how innovations in architectural writing and practice transformed an early modern sense of interiority. The book launches from a matrix of related “platforms”—a term that in early modern usage denoted scaffolds, stages, and draftsmen’s sketches—to situate Alberti, Shakespeare, Jonson, and others within a landscape of spatial and visual change. As the English house underwent a process of inward folding, replacing a logic of central assembly with one of dissemination, the subject who negotiated this new scenography became a flashpoint of conflict in both domestic and theatrical arenas. Combining theory with archival findings, Mimi Yiu reveals an emergent desire to perform subjectivity, to unfold an interior face to an admiring public. Highly praised for its lucid writing, comprehensive supplementary material, and engaging tone, Architectural Involutions was the winner of the 2016 MLA Prize for Independent Scholars.