본문 바로가기
KERD
논문KCI 등재

Connected Lie groups with many locally bounded finite-dimensional representations are linear

A. I. Shtern
장전수학회 (Jangjeon Mathematical Society)|2011.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제14권 제2호|pp. 183-188|DOI 10.17777/pjms.2011.14.2.001

2

조회

0

다운로드

2

인용

0

참고문헌

주제분류수학

초록

In this paper, it is proved that the following conditions are equivalent for any connected Lie group:(i) G admits sufficiently many locally bounded (not necessarily continuous) finite-dimensional representations;(ii) G admits a faithful locally bounded (not necessarily continuos) finite-dimensional representation;(iii) G admits sufficiently many continuous finite-dimensional representations;(iv) G admits a continuous faithful finite-dimensional representation, i.e., G is a linear Lie group. The equivalence (iv)⇔(i) is somewhat surprising.

Abstract

In this paper, it is proved that the following conditions are equivalent for any connected Lie group:(i) G admits sufficiently many locally bounded (not necessarily continuous) finite-dimensional representations;(ii) G admits a faithful locally bounded (not necessarily continuos) finite-dimensional representation;(iii) G admits sufficiently many continuous finite-dimensional representations;(iv) G admits a continuous faithful finite-dimensional representation, i.e., G is a linear Lie group. The equivalence (iv)⇔(i) is somewhat surprising.

참고문헌 (22)

  1. G. Birkhoff, "Lie groups simply isomorphic with no linear group", Bull. Amer. Math. Soc, 42, pp.883~888 (1936)
  2. M. Goto, "Faithful representations of Lie groups, I", Math. Japonicae, 1, pp.107~119 (1948)
  3. M. Goto, "Faithful representations of Lie groups, II", Nagoya Math. J, 1, pp.91~107 (1950)
  4. Harish-Chandra, "On faithful representations of Lie groups", Proc. Amer. Math.-Soc, 통권 : 1, pp.205~210 (1950)
  5. G. P. Hochschild, "The Structure of Lie Groups" (1965), Holden-Day
  6. G. P. Hochschild, "The universal representation kernel of a Lie group", Proc. Amer. Math. Soc, 통권 : 11, pp.625~629 (1960)
  7. G. P. Hochschild, "Complexification of real analytic groups", Trans. Amer. Math. Soc, 125, pp.406~413 (1966)
  8. D. Luminet, "Faithful uniformly continuous representations of Lie groups", J. London Math. Soc. (2), 49(1), pp.100~108 (1994)
  9. A. I. Mal'cev, "On linear connected locally-closed groups", Acad. Sci. URSS (N. S.), 40, pp.87~89 (1943)
  10. M. Moskowitz, "A remark on faithful representations", Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur, 52(8), pp.829~831 (1973)
  11. M. Moskowitz, "Faithful representations and a local property of Lie groups", Math. Z, 143, pp.193~198 (1975)
  12. A. I. Shtern, "Van der Waerden's continuity theorem for the commutator subgroups of connected Lie groups and Mishchenko's conjecture", Advanced Studies in Contemporary Mathematics, 13(2), pp.143~158 (2006), 장전수학회
  13. A. I. Shtern, "A version of the van der Waerden theorem and the proof of the Mishchenko conjecture for homomorphisms of locally compact groups", Izv. Math, 72(1), pp.169~205 (2008)
  14. Alexander I. Shtern, "APPLICATIONS OF AUTOMATIC CONTINUITY RESULTS TO ANALOGS OF THE FREUDENTHAL–WEIL AND HOCHSCHILD THEOREMS", Advanced Studies in Contemporary Mathematics, 20(2), pp.203~212 (2010), 장전수학회
  15. A. I. Shtern, "Connected locally compact groups: Hochschild kernel and the faithfulness of locally bounded finite-dimensional representations", ~
  16. A. I. Shtern, "Hochschild kernel for locally bounded finite-dimensional representations of a connected Lie group", Appl. Math. Comput (2011)
  17. N.S, "1945", 16(58)
  18. Alexander I. Shtern, "VON NEUMANN KERNEL OF A CONNECTED LOCALLY COMPACT GROUP, REVISITED", Advanced Studies in Contemporary Mathematics, 20(3), pp.313~318 (2010), 장전수학회
  19. Shtern, "HOMOMORPHIC IMAGES OF CONNECTED LIE GROUPS IN COMPACT GROUPS", Advanced Studies in Contemporary Mathematics, 20(1), pp.1~6 (2010), 장전수학회
  20. A. I. Shtern, "Connected Lie groups having faithful locally bounded (not necessarily continuous) finite-dimensional representations", Russ. J. Math. Phys, 16(4), pp.566~567 (2009)
  21. Shtern, "FREUDENTHAL-WEIL THEOREM FOR ARBITRARY EMBEDDINGS OF CONNECTED LIE GROUPS IN COMPACT GROUPS", Advanced Studies in Contemporary Mathematics, 19(2), pp.157~164 (2009), 장전수학회
  22. Shtern, "FREUDENTHAL-WEIL THEOREM FOR ARBITRARY EMBEDDINGS OF CONNECTED LIE GROUPS IN COMPACT GROUPS", Advanced Studies in Contemporary Mathematics, 19(2), pp.157~164 (2009), 장전수학회

관련 논문AI추천

Not necessarily continuous locally bounded finite-dimensional irreducible representations of connected lie groupsA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제1호A criterion for the continuity of the restriction to the commutator subgroup of a locally bounded finite-dimensional representation of a connected Lie group with respect to the ordinary group topologyA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제1호Rigidity of the topology on the linear perfect connected Lie groupsA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제4호Not necessarily continuous locally bounded finite-dimensional indecomposable pseudorepresentations of connected Lie groupsA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제2호Not necessarily continuous locally bounded finite-dimensional representations of connected Lie groups with indecomposable restriction to the radicalA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제2호IRREDUCIBLE LOCALLY BOUNDED FINITE-DIMENSIONAL PSEUDOREPRESENTATIONS OF CONNECTED LIE GROUPSA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제3호

이 간행물의 다른 논문 (9건)

On a four-parameter type I generalized half logistic distributionA. K. Olapadepp. 189-198On the k-dimensional generalization of q-Bernstein polynomials김태균, 최종성, 김영희pp. 199-208Graph equations for line graphs, middle graphs, semi-splitting block graphs and semi-line splitting block graphsV. Mathadpp. 209-214On q-Bernstein and q-Hermite polynomials최종성, C. S. Ryoo, T. Kim, 김영희pp. 215-222On a type of semi-symmetric non metric connection in Lorentzian para-Sasakian manifoldE. Yasarpp. 223-230
원문 보기