UNIVERSAL APPROACH TO THE TAKESAKI-TAKAI γ-DUALITY

被引:0
|
作者
Yaremenko, Mykola Ivanovich [1 ]
机构
[1] Tech Univ Ukraine, Dept PDE, 37 Prospect Beresteiskyi, UA-03056 Kyiv, Ukraine
来源
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2024年 / 14卷 / 05期
关键词
Takai duality; gamma-duality; Wigner function; C & lowast; -algebra; Pontryagin duality; induced representation; cross product; PRODUCT SYSTEMS; ASTERISK; CORRESPONDENCES;
D O I
10.11948/20230242
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, we generalize and simplify the proof of the TakesakiTakai 7-duality theorem. Assume a morphism omega : G Ant (A) is a projective representation of the locally compact Abel group G in Ant (A), mapping 7 : G G is continuous, and (A, , G, omega ) is a dynamic system then there exists isomorphism gamma (L 1 ( Upsilon : Env omega A circle times LK (L2 2 ( G ) ) G, , Env omega gamma(L1 omega gamma (L 1 ( G, A) ))) which is the equivariant for the double dual action (gamma gamma ( omega : G Ant L1 1 (gamma gamma (L1 1 ( G, A) )))) Env omega G, omega G , Env omega omega . These results deepen our understanding of the representation theory and are especially interesting given their possible applications to problems of the quantum theory.
引用
收藏
页码:2643 / 2652
页数:10
相关论文
共 50 条
  • [21] Gorenstein duality and universal coefficient theorems
    Davis, Donald M.
    Greenlees, J. P. C.
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2023, 227 (05)
  • [22] DUALITY OF TBP, THE UNIVERSAL TRANSCRIPTION FACTOR
    STRUHL, K
    SCIENCE, 1994, 263 (5150) : 1103 - 1104
  • [23] Universal duality in conic convex optimization
    Schurr, Simon P.
    Tits, Andre L.
    O'Leary, Dianne P.
    MATHEMATICAL PROGRAMMING, 2007, 109 (01) : 69 - 88
  • [24] Pivot duality of universal interpolation and extrapolation spaces
    Bargetz, Christian
    Wegner, Sven-Ake
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 460 (01) : 321 - 331
  • [25] Duality of patterning: Absolute universal or statistical tendency?
    Blevins, Juliette
    LANGUAGE AND COGNITION, 2012, 4 (04) : 275 - 296
  • [26] Universal Series for Hilbert Schemes and Strange Duality
    Johnson, Drew
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2020, 2020 (10) : 3130 - 3152
  • [27] STATISTICAL APPROACH AND DUALITY
    JENKOVSZKY, LL
    TRUSHEVSKY, AA
    SERTORIO, L
    LETTERE AL NUOVO CIMENTO, 1976, 15 (06): : 200 - 202
  • [28] DUALITY IN UNIVERSAL ALGEBRA .2. PRELIMINARY REPORT
    FAJTLOWI.S
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (01): : A47 - A47
  • [29] Poincare duality complexes with highly connected universal cover
    Bleile, Beatrice
    Bokor, Imre
    Hillman, Jonathan A.
    ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2018, 18 (07): : 3749 - 3788
  • [30] Universal duality in a Luttinger liquid coupled to a generic environment
    Yurkevich, Igor V.
    Yevtushenko, Oleg M.
    PHYSICAL REVIEW B, 2014, 90 (11)