Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

DECOMPOSITION THEOREMS OF LIE OPERATOR ALGEBRAS

  • Chen, Yin (School of Mathematics and Statistics Northeast Normal University) ;
  • Chen, Liangyun (School of Mathematics and Statistics Northeast Normal University)
  • Received : 2010.06.26
  • Published : 2011.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce a notion of Lie operator algebras which as a generalization of ordinary Lie algebras is an analogy of operator groups. We discuss some elementary properties of Lie operator algebras. Moreover, we also prove a decomposition theorem for Lie operator algebras.

Keywords

References

  1. C. W. Ayoub, Sylow theory for a certain class of operator groups, Canad. J. Math. 13 (1961), 192-200. https://doi.org/10.4153/CJM-1961-016-0
  2. R. Baer, Direct decompositions, Trans. Amer. Math. Soc. 62 (1947), 62-98. https://doi.org/10.1090/S0002-9947-1947-0021947-7
  3. R. Baer, Automorphism rings of primary Abelian operator groups, Ann. of Math. (2) 44 (1943), 192-227. https://doi.org/10.2307/1968763
  4. G. Glauberman, Fixed points in groups with operator groups, Math. Z. 84 (1964), 120-125. https://doi.org/10.1007/BF01117119
  5. F. Gross, A note on fixed-point-free solvable operator groups, Proc. Amer. Math. Soc. 19 (1968), 1363-1365. https://doi.org/10.1090/S0002-9939-1968-0231909-1
  6. N. Jacobson, Basic Algebra II, W. H. Freeman and Company, San Francisco, 1980.
  7. C. Jiang, D. Meng, and S. Q. Zhang, Some complete Lie algebras, J. Algebra 186 (1996), no. 3, 807-817. https://doi.org/10.1006/jabr.1996.0396
  8. D. Meng and S. Wang, On the construction of complete Lie algebras, J. Algebra 176 (1995), no. 2, 621-637. https://doi.org/10.1006/jabr.1995.1263
  9. D. Robinson, A Course in the Theory of Groups, Springer-Verlag, New York, 1982.
  10. S. Suanmali, On the relationship between the class of a Lie algebra and the classes of its subalgebras, Internat. J. Algebra Comput. 18 (2008), no. 1, 83-95. https://doi.org/10.1142/S0218196708004275
  11. Y. Wang, Finite groups admitting a p-solvable operator group, J. Algebra 204 (1998), no. 1, 478-490.
  12. T. Wolf, Character correspondences induced by subgroups of operator groups, J. Algebra 57 (1979), no. 2, 502-521. https://doi.org/10.1016/0021-8693(79)90236-9