Seul Hee Choi

Derivations of a Restricted Weyl-Type Algebra Containing the Polynomial Ring

A Weyl type nonassociative algebra and its subalgebra have been defined in the articles Choi and Nam (2005a b c); Lee and Nam (2004). Several authors have found all the derivations of some given algebra (see Ahmadi et al., 2005; Choi and Nam, 2005b; Kac, 1974; Kirkman et al., 1994; Osborn, 1997; Osborn and Passman, 1995). In this article, we find all derivations of the nonassociative algebra and show that the dimension of all derivations of the algebra is (s 1 + s 2)2 + s 1 + s 2. Because of the dimension of a derivation algebra, we know that if s 1 + s 2 ≠ s 1′ + s 2′, then the algebras and are not isomorphic.

Weyl Type Non-Associative Algebras Using Additive Groups I

A Weyl type algebra is defined in the book [4]. A Weyl type non-associative algebra and its restricted subalgebra are defined in various papers (see [1, 3, 11, 12]). Several authors find all the derivations of an associative (a Lie, a non-associative) algebra (see [1, 2, 4, 6, 11, 12]). We define the non-associative simple algebra and the semi-Lie algebra , where . We prove that the algebra is simple and find all its non-associative algebra derivations.

Degree Stable Lie Algebras I

We define a degree stable Lie algebra. Since the special type Lie algebra S+(2) is degree stable, we find the automorphism group AutLie(S+(2)) of the Lie algebra S+(2) and prove the Jacobian conjecture of the Lie algebra S+(2).

Non-associative Algebras with n-Exponential Functions

Dernon(𝔽[x1, x2, …, xn]Mn) of the evaluation algebra 𝔽[x1, x2, …, xn]Mn and Dernon(𝔽[e± x1, e± x2, …, e± xn]Mn) of the evaluation algebra 𝔽[e± x1, e± x2, …, e± xn]Mn are found in [2] and [4], respectively, where Mn = {∂1, …, ∂n}. In this work we find of the algebra . We define a finite dimensional semi-Lie algebra which is simple. We define a simple semi-Lie ring whose dimension is finite.

Combinatorial Algebra and Its Antisymmetrized Algebra I

The simple non-associative algebra N(eAS, q, n, t)k and its simple subalgebras are defined in [1, 3, 5–7, 13]. In this work, we define the combinatorial algebra N(e𝔄p, n, t)k and its antisymmetrized algebra and their subalgebras. We prove that these algebras are simple. Some authors [2, 5–7, 10, 13, 14, 16, 17] found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra. We find all the derivations of the subalgebra N(e±x1x2 ⋯xn, 0, n)[1] of N(e𝔄p, n, t)k and the Lie subalgebra of .

Automorphism Group of a Special Type Lie Algebra I

In an earlier paper, we defined a degree stable Lie algebra, and determined the Lie algebra automorphism group AutLie(S+(2)) of the Lie algebra S+(2). In this paper, we determine the Lie algebra automorphism group AutLie(S(1,0,2)) of the Lie algebra S(1,0,2).

Algebra Versus Its Anti-symmetric Algebra

For a given algebra A= 〈A,+,·〉, we can define its anti-symmetric algebra A-= 〈A-,+,[ , ]〉 using the commutator [ , ] of A, where the sets A and A- are the same. We show that there are isomorphic algebras A1 and A2 such that their anti-symmetric algebras are not isomorphic. We define a special type Lie algebra and show that it is simple.

The Robinson-Schensted correspondence for skew oscillating semi-standard tableaux

We introduce an analogue of the Robinson-Schensted correspondence for skew oscillating semi-standard tableaux that generalizes the correspondence for skew oscillating standard tableaux. We give a geometric construction for skew oscillating semi-standard tableaux and examine its combinatorial properties.

Counting lattice paths in restricted planes

Abstract The number of lattice paths of fixed length consisting of unit steps in the north, south, east or west directions in the plane {(x,y)∈ R 2 | 0⩽y⩽x} is shown. Also, the paths which do not cross the line y =− x + a for a positive integer a, in the plane {(x,y)∈ R 2 | 0⩽y⩽x} are enumerated. The proofs are purely combinatorial, using the bijections, the technique of the enumeration of noncrossing paths and the reflection principle.