Linear Representation of Groups. Ernest B. Vinberg. Publisher In a compact orbit of less than 150 pages, so to speak, Vinberg covers the basic theory of representations of finite, compact, and Lie groups, the author's aim being "to give as simple and detailed an account as possible of the problems A linear representation ? of G on a complex vector space V is a set-theoretic action on V which preserves the linear structure, that is Today we discuss the representations of a cyclic group, and then proceed to dene the important notions of irreducibility and complete reducibility. Linear Representations of Groups book. Read reviews from world's largest community for readers. Linear Representations by E.B. Vinberg. The linear groups which are obtained in this manner are called ?-groups in this paper; they have certain properties which are analogous to properties of We generalize the basic results of Vinberg's ?-groups, or periodically graded reductive Lie algebras, to fields of good positive characteristic. A representation of a group G on a complex vector space V is a group action of G on V by linear transformations, i.e., a homomorphism of G into Later when representation theory was extended to Lie groups and when quantum mechanics forced infinite-dimensional representations into the study Representation theory is the branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, as well as modules over these abstract algebraic structures. The main goal is to represent the group in question in a concrete way. E. B. Vinberg. Full text: PDF file (1707 kB). E. B. Vinberg, "Some examples of crystallographic groups in Lobachevskii spaces", Math. E. B. Vinberg, "Discrete linear groups generated by reflections", Math. USSR-Izv., 5:5 (1971), 1083-1119. Linear representations of groups by Vinberg, E. B., 1989, Birkhauser Verlag edition, in English. Are you sure you want to remove Linear representations of groups from your list? Linear Representations of Groups Vinberg Springer 9783034800624 : This book presents a comprehensive and detailed exposition of the fundamentals of the representation theory of groups, especia. Linear Representations of Groups, Vinberg. Варианты приобретения. Linear Representations of Groups : Translated from the Russian by A. Iacob. by Ernest B. Vinberg. This book gives an exposition of the fundamentals of the theory of linear representations of ?nite and compact groups, as well as elements of the t- ory of linear representations of Lie Vinberg has written an algebra book that is excellent, both as a classroom text or for self-study. It starts with the most basic concepts and builds in orderly fashion to moderately advanced topics Well motivated examples help the student to master the material thoroughly, and exercises test one's Vinberg has written an algebra book that is excellent, both as a classroom text or for self-study. It starts with the most basic concepts and builds in orderly fashion to moderately advanced topics Well motivated examples help the student to master the material thoroughly, and exercises test one's Representations of nite groups Representations of groups on vector spaces, matrix representations. Equivalence of represen-tations. Invariant subspaces and submodules. Irreducibility and Schur's Lemma. Complete reducibility for nite groups. Linear