• 제목/요약/키워드: algebraically closed field

검색결과 29건 처리시간 0.017초

Lie Algebras with all $\underline{1}$-filtrations

  • Jung, K.S.
    • 충청수학회지
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    • 제7권1호
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    • pp.75-86
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    • 1994
  • Let L be a Lie algebra over an algebraically closed field F of chracteristic p > 0 which has an $\underline{1}$-filtration. We prove that W(1;$\underline{1}$) is the only restricted simple Lie algebra having an $\underline{1}$-filtration. And we show that the even dimensional Lie algebra can not have an $\underline{1}$-filtration.

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ON SUBREGULAR POINTS FOR SOME CASES OF LIE ALGEBRA

  • KIM, Y.K.;SO, K.H.;SEO, G.S.;PARK, D.Y.;CHOI, S.H.
    • 호남수학학술지
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    • 제19권1호
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    • pp.21-27
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    • 1997
  • We shall define three kinds of points for algebraic varieties associated to the center 3 of U(L) which is the universal enveloping algebra of a finite-dimensional modular Lie algebra over an algebraically closed field F of prime characteristic p. We announce here that $sp_4$(F) with p = 2 has a subregular point.

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Class function table matrix of finite groups

  • Park, Won-Sun
    • 대한수학회지
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    • 제32권4호
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    • pp.689-695
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    • 1995
  • Let G be a finite group with k distinct conjugacy classes $C_1, C_2, \cdots, C_k$ and F an algebraically closed field such that char$(F){\dag}\left$\mid$ G \right$\mid$$. We denoted by $Irr_F$(G) the set of all irreducible F-characters of G and $Cf_F$(G) the set of all class functions of G into F. Then $Cf_F$(G) is a commutative F-algebra with an F-basis $Irr_F(G) = {\chi_1, \chi_2, \cdots, \chi_k}$.

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A Study on the Relationship between Properties of the Elliptic Curves and Performance of Elliptic Curve Method (ECM)

  • Jizhe Cui;Shin, Seung-won;Park, Jong-Uk
    • 한국지능정보시스템학회:학술대회논문집
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    • 한국지능정보시스템학회 2000년도 춘계정기학술대회 e-Business를 위한 지능형 정보기술 / 한국지능정보시스템학회
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    • pp.475-478
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    • 2000
  • Recently encryption algorithms based on difficulties of factorization have been used with popularization. Prime number factorizations are progressed rapidly. In this paper, characteristics of elliptic curve are analyzed and generation of elliptic curves suitable for prime number factorization is discussed.

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SUBREGULAR POINTS FOR SOME CASES OF LIE ALGEBRAS

  • KIM, Y.K.;SO, K.H.;JEONG, J.W.;PARK, D.Y.;CHOI, S.H.
    • 호남수학학술지
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    • 제21권1호
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    • pp.75-95
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    • 1999
  • Dimensions of irreducible $so_5(F)$-modules over an algebraically closed field F of characteristics p > 2 shall be obtained. It turns out that they should be coincident with $p^{m}$, where 2m is the dimension of coadjoint orbits of ${\chi}{\in}so_5(F)^*{\backslash}0$ as Premet asserted. But there is no subregular point for $g=sp_4(F)=so_5(F)$ over F.

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ON IRREDUCIBILITY OF INDUCED MODULES AND AN ADAPTATION OF THE WIGNER-MACKEY METHOD OF LITTLE GROUPS

  • Venkataraman, Geetha
    • 대한수학회지
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    • 제50권6호
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    • pp.1213-1222
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    • 2013
  • This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group G over a field $\mathbb{K}$ where the group G is a semidirect product of a normal abelian subgroup N and a subgroup H. The main results are proved with the assumption that char $\mathbb{K}$ does not divide |G| but there is no assumption made of $\mathbb{K}$ being algebraically closed.

SOME REMARKS ON FOUR KINDS OF POINTS ASSOCIATED TO LIE ALGEBRAS

  • KIM, Y.K.;SO, K.H.;SEO, G.S.;PARK, D.Y.;CHOI, S.H.
    • 호남수학학술지
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    • 제20권1호
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    • pp.31-43
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    • 1998
  • Exact definitions of four kinds of points shall be defined associated to Lie algebras L over an algebraically closed field F of prime characteristic p > 0. Next, rough bound of dimensions for L-irreducible modules associated to subregular points shall be established by taking advantage of Premet's result.

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