692 research outputs found

    A note on free differential graded algebra resolutions

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    We work ove a field k. A differential graded algebra(dga for short) in this paper is a praded k-algebra U=[?] Un with diffrential d of degree-1. Given a k-algebra R, it is well-known that there exists a free dga resolution ..

    Chern classes of multiplicative direct image of vector bundles

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    日本語と朝鮮語の時制と相

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    現在時制の日本語の動詞と冠形詞形の基本形は未來時制に使われる傾向が多い.動作が完了し,結果が目前にある時は,‘ている’で表現する.これは,朝鮮語は進行相と狀態の結果の表現があるが,日本語は一つしか無い為である.又,朝鮮語‘었(았 , 였)’には現在の狀態を表す機能があるが,日本語‘た’にはその機能は無い.‘어(아 , 여) 있다’に置き変えられる‘었(았 , 였)’は‘ている’を使う.又,‘た’は,過去以外に完了と,發見の機能がある.朝鮮語は‘아직 + 過去形’が可能だが,日本語は過去形は不可能である.朝鮮語で‘었’が重複した‘었었’の場合,日本語は‘ていた’の表現になる.研究論

    Central Invariants and Frobenius-Schur Indicators for Semisimple Quasi-Hopf Algebras

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    In this paper, we obtain a canonical central element νH\nu_H for each semi-simple quasi-Hopf algebra HH over any field kk and prove that νH\nu_H is invariant under gauge transformations. We show that if kk is algebraically closed of characteristic zero then for any irreducible representation of HH which affords the character χ\chi, χ(νH)\chi(\nu_H) takes only the values 0, 1 or -1, moreover if HH is a Hopf algebra or a twisted quantum double of a finite group then χ(νH)\chi(\nu_H) is the corresponding Frobenius-Schur Indicator. We also prove an analog of a Theorem of Larson-Radford for split semi-simple quasi-Hopf algebra over any field kk. Using this result, we establish the relationship between the antipode SS, the values of χ(νH)\chi(\nu_H), and certain associated bilinear forms when the underlying field kk is algebraically closed of characteristic zero.Comment: 32 pages (version 3

    NOVAMENTE ORDEM E PROGRESSO?

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    A divisa Ordem e Progresso representa uma das ideias motoras da ideologia positivista, particularmente a de cunho comtiano. Reincidentemente esta formulação doutrinária tem aparecido mostrando, sob certo aspecto, a “fecundidade” deste ideário no sentido de legitimar uma dada concepção de mundo. O caráter autoritário e conservador inerente a esta divisa tem demonstrado quão útil tem sido sua utilização como uma efetiva violência simbólica no sentido de conseguir uma anuência consentida dos dominados ao projeto sócio-político das elites. De modo que o ressurgimento deste dístico como aparato publicitário revela que o projeto conservador da classe dominante brasileira continua presente. Este trabalho analisa alguns aspectos da natureza e constituição do lema “Ordem e Progresso” com ênfase na assunção efetuada pela corrente filiada às formulações ortodoxas de Augusto Comte

    The Grothendieck ring of vector spaces with two idempotent endomorphisms

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    In this paper we are concerned with a paticular bialgebra Λ over a field k, which is generated as an algebra by e1, e2 with defining relations e2/3=e1, e2/2=e2, and whose comultiplication ..

    Monoidal 2-structure of Bimodule Categories

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    We define a notion of tensor product of bimodule categories and prove that with this product the 2-category of C-bimodule categories for fixed tensor C is a monoidal 2-category in the sense of Kapranov and Voevodsky. We then provide a monoidal-structure preserving 2-equivalence between the 2-category of C-bimodule categories and Z(C)-module categories (module categories over the center). For finite group G we show that de-equivariantization is equivalent to tensor product over category Rep(G) of finite dimensional representations. We derive Rep(G)-module fusion rules and determine the group of invertible irreducible Rep(G)-module categories extending earlier results for abelian groups.Comment: 40 pages, minor errors corrected, references added. To appear in J. Algebr

    Weakly group-theoretical and solvable fusion categories

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    We introduce two new classes of fusion categories which are obtained by a certain procedure from finite groups - weakly group-theoretical categories and solvable categories. These are fusion categories that are Morita equivalent to iterated extensions (in the world of fusion categories) of arbitrary, respectively solvable finite groups. Weakly group-theoretical categories have integer dimension, and all known fusion categories of integer dimension are weakly group theoretical. Our main results are that a weakly group-theoretical category C has the strong Frobenius property (i.e., the dimension of any simple object in an indecomposable C-module category divides the dimension of C), and that any fusion category whose dimension has at most two prime divisors is solvable (a categorical analog of Burnside's theorem for finite groups). This has powerful applications to classification of fusion categories and semsisimple Hopf algebras of a given dimension. In particular, we show that any fusion category of integer dimension <84 is weakly group-theoretical (i.e. comes from finite group theory), and give a full classification of semisimple Hopf algebras of dimensions pqr and pq^2, where p,q,r are distinct primes.Comment: 28 pages, latex; added many references and details in proof
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