• Honam Mathematical Journal
• /
• v.17 no.1
• /
• pp.7-14
• /
• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)

• Journal of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.427-442
• /
• 2014

A previous work gave a combinatorial description of the crystal B(${\infty}$), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present an explicit description of the crystal B(${\lambda}$), in terms of the marginally large tableaux, for the $G_2$ Lie algebra type. We also provide a new description of B(${\lambda}$), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.

• Kyungpook Mathematical Journal
• /
• v.48 no.2
• /
• pp.223-232
• /
• 2008

We estimate the real rank of CCR C*-algebras under some assumptions. A applications we determine the real rank of the reduced group C*-algebras of non-compac connected, semi-simple and reductive Lie groups and that of the group C*-algebras of connected nilpotent Lie groups.

• Journal of the Korean Mathematical Society
• /
• v.48 no.1
• /
• pp.117-132
• /
• 2011

By developing a linear algebra program involving many different structures associated to a three-graded H*-algebra, it is shown that if L is a Lie triple automorphism of an infinite-dimensional topologically simple associative H*-algebra A, then L is either an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism. If A is finite-dimensional, then there exists an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism F : A $\rightarrow$ A such that $\delta$:= F - L is a linear map from A onto its center sending commutators to zero. We also describe L in the case of having A zero annihilator.

• Honam Mathematical Journal
• /
• v.36 no.1
• /
• pp.179-186
• /
• 2014

In this paper, we consider the simple non-associative algebra $\overline{WN(\mathbb{F}[e^{{\pm}x^r},0,1]_{(\partial,\partial^2)})}$. There are many papers on finding the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [2], [3], [4], [5], [6], [7], [12], [14]). We find all the derivations of the algebra $\overline{WN(\mathbb{F}[e^{{\pm}x^r},0,1]_{(\partial,\partial^2)})}$.

• Journal of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.711-725
• /
• 2008

We give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite-dimensional irreducible representations of the simple Lie algebra $sp_4$. We also identify the monomial basis consisting of the reduced monomials with a set of semistandard tableaux of a given shape, on which we give a colored oriented graph structure.

• Honam Mathematical Journal
• /
• v.29 no.2
• /
• pp.269-277
• /
• 2007

Let L := L(G) denote the classical modular Lie algebra of $E_6$-type over an algebraically closed field F of characteristic p > 5 associated with some simple and simply connected algebraic group G. After the prototypes of those for $E_8$-type in [4], we shall search for irreducible (=simple) L-modules in this paper.

• Honam Mathematical Journal
• /
• v.31 no.3
• /
• pp.407-419
• /
• 2009

The simple non-associative algebra $N(e^{A_S},q,n,t)_k$ and its simple sub-algebras are defined in the papers [1], [3], [4], [5], [6], [12]. We define the non-associative algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$ and its antisymmetrized algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$. We also prove that the algebras are simple in this work. There are various papers on finding all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [3], [5], [6], [9], [12], [14], [15]). We also find all the derivations $Der_{anti}(WN(e^{{\pm}x^r},0,2)_B^-)$ of te antisymmetrized algebra $WN(e^{{\pm}x^r}0,2)_B^-$ and every derivation of the algebra is outer in this paper.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.627-634
• /
• 2006

A Weyl type algebra is defined in the book ([4]). A Weyl type non-associative algebra $\={WP_{m,n,s}}$ and its restricted sub-algebra $\={WP_{m,n,s_{\gamma}}}$ are defined in various papers ([1], [12], [3], [11]). Several authors 0nd all the derivations of an associative (Lie or non-associative) algebra in the papers ([1], [2], [12], [4], [6], [11]). We find all the non-associative algebra derivations of the non-associative algebra $\={WP_{0,2,0_B}$, where $B=\{{\partial}_0,\;{\partial}_1,\;{\partial}_2,\;{\partial}_{12},\;{\partial}^2_1,\;{\partial}^2_2\}$.

• Honam Mathematical Journal
• /
• v.27 no.4
• /
• pp.583-593
• /
• 2005

The Weyl-type non-associative algebra ${\overline{WN_{g_n,m,s_r}}$ and its subalgebra ${\overline{WN_{n,m,s_r}}$ are defined and studied in the papers [2], [3], [9], [11], [12]. We find the derivation group $Der_{non}({\overline{WN_{1,0,0_{[2]}}})$ the non-associative simple algebra ${\overline{WN_{1,0,0_{[2]}}}$.