• Title/Summary/Keyword: exterior algebra

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CAUCHY DECOMPOSITION FORMULAS FOR SCHUR MODULES

  • Ko, Hyoung J.
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.41-55
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    • 1992
  • The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

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CLIFFORD $L^2$-COHOMOLOGY ON THE COMPLETE $K\"{A}$HLER MANIFOLDS

  • Pak, Jin-Suk;Jung, Seoung-Dal
    • Journal of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.167-179
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    • 1997
  • In the study of a manifold M, the exterior algebra $\Lambda^* M$ plays an important role. In fact, the de Rham cohomology theory gives many informations of a manifold. Another important object in the study of a manifold is its Clifford algebra (Cl(M), generated by the tangent space.

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ON THE CHARACTER RINGS OF TWIST KNOTS

  • Nagasato, Fumikazu
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.3
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    • pp.469-474
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    • 2011
  • The Kauffman bracket skein module $K_t$(M) of a 3-manifold M becomes an algebra for t = -1. We prove that this algebra has no non-trivial nilpotent elements for M being the exterior of the twist knot in 3-sphere and, therefore, it is isomorphic to the $SL_2(\mathbb{C})$-character ring of the fundamental group of M. Our proof is based on some properties of Chebyshev polynomials.

The structure conformal vector fields on a sasakian manifold II

  • Hyun, Jong-Ik
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.661-679
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    • 1995
  • The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

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COMMUTING POWERS AND EXTERIOR DEGREE OF FINITE GROUPS

  • Niroomand, Peyman;Rezaei, Rashid;Russo, Francesco G.
    • Journal of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.855-865
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    • 2012
  • Recently, we have introduced a group invariant, which is related to the number of elements $x$ and $y$ of a finite group $G$ such that $x{\wedge}y=1_{G{\wedge}G}$ in the exterior square $G{\wedge}G$ of $G$. This number gives restrictions on the Schur multiplier of $G$ and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form $h^m{\wedge}k$ of $H{\wedge}K$ such that $h^m{\wedge}k=1_{H{\wedge}K}$, where $m{\geq}1$ and $H$ and $K$ are arbitrary subgroups of $G$.

INVARIANTS OF THE SYMMETRIC GROUP

  • Lee, Hyang-Sook
    • Communications of the Korean Mathematical Society
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    • v.10 no.2
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    • pp.293-300
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    • 1995
  • Let $R = k[y_1,\cdots,y_n] \otimes E[x_1, \cdots, x_n]$ with characteristic $k = p > 2$ (odd prime), where $$\mid$y_i$\mid$ = 2, $\mid$x_i$\mid$ = 1$ and $y_i = \betax_i, \beta$ is the Bockstein homomorphism. Topologically, $R = H^*(B(Z/p)^n,k)$. For a symmetric group $\sum_n, R^{\sum_n} = k[\sigma_1,\cdots,\sigma_n] \otimes E[d\sigma_1, \cdots, d\sigma_n]$ where d is the derivation satisfying $d(y_i) = x_i$ and $d(x_iy_i) = x_iy_i + x_jy_i, 1 \leq i, j \leq n$. We give a direct proof of this theorem by using induction.

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Three Characteristic Beltrami System in Even Dimensions (I): p-Harmonic Equation

  • Gao, Hongya;Chu, Yuming;Sun, Lanxiang
    • Kyungpook Mathematical Journal
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    • v.47 no.3
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    • pp.311-322
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    • 2007
  • This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.

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