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An Invariant for Locally Finite Dimensional Semisimple Algebras

1995 Algebra
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Release : 1995
Genre : Algebra
Kind : eBook
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Book Synopsis An Invariant for Locally Finite Dimensional Semisimple Algebras by : Hoan Duong

Download or read book An Invariant for Locally Finite Dimensional Semisimple Algebras written by Hoan Duong. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: The conjecture of (GH) concerning a proposed complete invariant for direct limit algebras is simplified, and we show that this invariant (essentially a diagram of ordered $K\sb0$-groups) is complete, establishing the conjecture.

Finite Dimensional Algebras

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 441/5 ( reviews)

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Book Synopsis Finite Dimensional Algebras by : Yurj A. Drozd

Download or read book Finite Dimensional Algebras written by Yurj A. Drozd. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This English edition has an additional chapter "Elements of Homological Al gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.

Trends in Ring Theory

1998 Rings (Algebra)
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Release : 1998
Genre : Rings (Algebra)
Kind : eBook
Book Rating : 498/5 ( reviews)

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Book Synopsis Trends in Ring Theory by : Vlastimil Dlab

Download or read book Trends in Ring Theory written by Vlastimil Dlab. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: The Ring Theory Conference, held a the University of Miskolc, Hungary, successfully accomplished its two goals: to reflect contemporary trends in the subject area; and to offer a meeting place for a large number of Eastern European algebraists and their colleagues from around the world. Particular emphasis was placed on recent developments in the following four areas: representation theory, group algebras, PI algebras and general ring theory. This book presents 13 of the invited lectures.

Invariant Means and Finite Representation Theory of C*-algebras

Mathematics
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Genre : Mathematics
Kind : eBook
Book Rating : 873/5 ( reviews)

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Book Synopsis Invariant Means and Finite Representation Theory of C*-algebras by : Nathanial Patrick Brown

Download or read book Invariant Means and Finite Representation Theory of C*-algebras written by Nathanial Patrick Brown. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: Various subsets of the tracial state space of a unital C$*$-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II$ 1$-factor representations of a class of C$*$-algebras considered by Sorin Popa are also studied. These algebras are shown to have an unexpected variety of II$ 1$-factor representations. In addition to developing some general theory we also show that these ideas are related to numerous other problems inoperator algebras.

Homological Invariants in the Representation Theory of Finite Dimensional Algebras

2011
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Release : 2011
Genre :
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Book Rating : 414/5 ( reviews)

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Book Synopsis Homological Invariants in the Representation Theory of Finite Dimensional Algebras by : Thomas Troy Howard

Download or read book Homological Invariants in the Representation Theory of Finite Dimensional Algebras written by Thomas Troy Howard. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: A lattice-valued version of complexity is introduced for finitely generated representations of finite dimensional algebras which measures the dimension growth of their syzygies. The spectrum of complexities over a finite dimensional algebra is shown to be invariant under derived equivalences in many instances. Directed graphs called "syzygy quivers" are used to explicitly compute complexity for representations of monomial algebras and to confirm that the spectrum of complexities of a monomial algebra is a derived invariant. "Relative complexity spectra" are used to show that this complexity spectrum is a derived invariant for any finite dimensional algebra which satisfies certain "translation invariance" properties. Examples of such algebras include Gorenstein algebras, local algebras, and commutative algebras; no example is known of an algebra which lacks this property.

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