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Thursday, July 30, 2020 | History

7 edition of Homology of classical groups over finite fields and their associated infinite loop spaces found in the catalog.

Homology of classical groups over finite fields and their associated infinite loop spaces

by Zbigniew Fiedorowicz

  • 396 Want to read
  • 25 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

    Subjects:
  • Linear algebraic groups.,
  • Homology theory.,
  • Finite fields (Algebra),
  • Infinite loop spaces.

  • Edition Notes

    StatementZbigniew Fiedorowicz, Stewart Priddy.
    SeriesLecture notes in mathematics ; 674, Lecture notes in mathematics (Springer-Verlag) ;, 674.
    ContributionsPriddy, Stewart, 1940- joint author.
    Classifications
    LC ClassificationsQA3 .L28 no. 674, QA171 .L28 no. 674
    The Physical Object
    Paginationvi, 434 p. ;
    Number of Pages434
    ID Numbers
    Open LibraryOL4724473M
    ISBN 100387089322
    LC Control Number78012091

    On the infinite loop space structure of the cobordism category Nguyen, Hoang Kim, Algebraic & Geometric Topology, ; Categorical models for equivariant classifying spaces Guillou, Bertrand, May, Peter, and Merling, Mona, Algebraic & Geometric Topology, ; Infinite loop spaces and nilpotent K–theory Adem, Alejandro, Gómez, José, Lind, John, and Tillmann, Ulrike, Algebraic & Geometric Cited by: Oct 30,  · Abstract: In this paper, we study the generalized (co)homology Hopf algebras of the loop spaces on the infinite classical groups, generalizing the work due to Kono-Kozima and Clarke. We shall give a description of these Hopf algebras in terms of symmetric functions. Based on topological considerations in the first half of this paper, we then introduce a universal analogue of the factorial Author: Masaki Nakagawa, Hiroshi Naruse.

    General linear group of a vector space. If V is a vector space over the field F, the general linear group of V, written GL(V) or Aut(V), is the group of all automorphisms of V, i.e. the set of all bijective linear transformations V → V, together with functional composition as group coopsifas.com V has finite dimension n, then GL(V) and GL(n, F) are isomorphic. Homology of classical groups over finite fields and their associated infinite loop spaces. Springer Lecture Notes in Mathematics Volume , I'm a little surprised this has not yet been mentioned, since it seems to give more complete answers than some that are cited above.

    Subalgebras of group cohomology defined by infinite loop spaces Article in Topology 44(4) · January with 2 Reads How we measure 'reads'. On the regularity conjecture for the cohomology of finite groups Groups Over Finite Fields and Their Associated Infinite Loop Spaces. categories of classical groups over finite fields.- K.


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Homology of classical groups over finite fields and their associated infinite loop spaces by Zbigniew Fiedorowicz Download PDF EPUB FB2

Coopsifas.com: Homology of Classical Groups Over Finite Fields and Their Associated Infinite Loop Spaces (Lecture Notes in Mathematics) (): Z. Fiedorowicz, S. Priddy: BooksAuthor: Z. Fiedorowicz. Homology of Classical Groups Over Finite Fields and Their Associated Infinite Loop Spaces. Authors; Zbigniew Fiedorowicz; Stewart Priddy; Book.

13 Citations; k Downloads; κ-theory of finite fields and the ImJ spaces. Zbigniew Fiedorowicz, Stewart Priddy. Pages Infinite loop spaces associated with ImJ --Permutative categories of classical groups over finite fields --K-theory of finite fields and the ImJ spaces --Calculations at the prime 2 --Calculations at odd primes --The homology of certain finite groups --Detection theorems at the prime 2 --Detection theorems at odd primes --Homology operations.

Sep 20,  · Z. Fiedorowicz and S. Priddy, Homology of classical groups over finite fields and their associated infinite loop spaces (to appear). Google ScholarCited by: 2. Aug 24,  · Homology of Classical Groups Over Finite Fields and Their Associated Infinite Loop Spaces pp | Cite asAuthor: Zbigniew Fiedorowicz, Stewart Priddy.

Homology of Classical Groups Over Finite Fields and Their Associated Infinite Loop Spaces pp | Cite asAuthor: Zbigniew Fiedorowicz, Stewart Priddy. Fiedorowicz and S. Priddy, Homology of classical groups over finite fields and their associated infinite loop spaces, Lecture Notes in Math., Author: J.

May. Roughly speaking, for each commutative ring R there are seven infinite classes of affine Kac-Moody groups over R, and to each infinite class we can associate an analogous infinite loop space.

Classical groups over general fields or algebras. Classical groups, more broadly considered in algebra, provide particularly interesting matrix groups.

When the field F of coefficients of the matrix group is either real number or complex numbers, these groups are just the classical Lie groups.

When the ground field is a finite field, then the classical groups are groups of Lie type. Homology of Classical Groups Over Finite Fields and Their Associated Infinite Loop Spaces (Lecture Notes in Mathematics) Oct 10, by Z.

Fiedorowicz, S. Priddy. Get this from a library. Homology of classical groups over finite fields and their associated infinite loop spaces. [Zbigniew Fiedorowicz; Stewart Priddy]. The above result is the only positive result on the homotopy invariance of Pontrjagin classes.

In contrast to results on topological invariance [8,6,10,1l], we shall see that integral or multiples of integral Pontrjagin classes are not homotopy invariant.

Rational Pontrjagin classes of stable bundles are not homotopy invariant [12], in fact, Cited by: 1. Z Fiedorowicz, S Priddy, Homology of classical groups over finite fields and their associated infinite loop spaces, Lecture Notes in MathematicsSpringer, Berlin () Mathematical Reviews (MathSciNet): MR Zentralblatt MATH: Cited by: 1.

The purpose of this note is to give a very simple proof of Karoubi's conjecture for finite fields. The proof is based on (1) and the close relationship between the classical groups over finite fields and the continuous classical groups [3, Let GL„(Fq) be the general linear group of invertible n x n matrices over Fq, a finite coopsifas.com by: 2.

maps in the homotopy class of some f0 are called infinite loop spaces and infinite loop maps. The suspension 2A" of a based space X is the smash product X /\S\ where X /\ Y is the quotient of X X Y by the wedge, or 1-point union, X V Y.

The nth stable homotopy group irs nX of X is the direct limit of the groups ir„+J2 JX. by a genius named John Nash will live longer than any finite characteristic. FIEDOROWICZ AND S. PRIDDY, Homology of Classical Groups over Finite Fields and Their Associated Infinite Loop Spaces, Springer,pp. An awesome new machinery is conquering mathematics.

It is called K-theory. Despite the. The homotopy type of BG 2 Λ for some small matrix groups G. Homology of Classical Groups Over Finite Fields and Their Associated Infinite Loop Spaces Homology operations associated with.

Subalgebras of group cohomology defined by infinite loop spaces. Author links open overlay panel J.R. Hunton a B. Schuster b. Show more. Specialising to classifying spaces of finite groups and F p coefficients, we now prove the main theorem,of the section. In fact, we offer two proofs, both resting on the stabilisation results just Cited by: 2.

Get this from a library. Homology of classical groups over finite fields and their associated infinite loop spaces. [Zbigniew Fiedorowicz; Stewart Priddy; SpringerLink (Service en ligne)]. Oct 24,  · Torsion classes in the cohomology of congruence subgroups - Volume Issue 2 - Dominique Arlettaz Exponents for extraordinary homology groups.

Commentarii Mathematici Helvetici, Vol. 68, Issue. 1, p. Homology of Classical groups over Finite Fields and their associated Infinite Loop coopsifas.com by: 7. Z Fiedorowicz, S Priddy, Homology of classical groups over finite fields and their associated infinite loop spaces, Lecture Notes in Math.Springer, Berlin () Mathematical Reviews (MathSciNet): MR Zentralblatt MATH: Cited by: In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological coopsifas.comgy groups were originally defined in algebraic coopsifas.comr constructions are available in a wide variety of other contexts, such as abstract algebra, groups, Lie algebras, Galois theory, and algebraic.Get this from a library!

Homology of Classical Groups Over Finite Fields and Their Associated Infinite Loop Spaces.