A Class of Nongraded Simple Lie Algebras

Abstract

Nongraded simple Lie algebras appear naturally in mathematical physics. In this paper, a new class of nongraded simple Lie algebras are presented based on the pairs (𝒜, 𝒟) consisting of a commutative associative unital algebra 𝒜 and a finite dimensional commutative derivation subalgebra 𝒟 such that 𝒜 is 𝒟-simple. The isomorphism classes of these nongraded Lie algebras are also determined and the structure space of these algebras is given explicitly.     

On Units of Group Algebras of 2-Groups of Maximal Class

Abstract

We determine the number of elements of order two in the group of normalized units V(𝔽₂ G) of the group algebra 𝔽₂ G of a 2-group of maximal class over the field 𝔽₂ of two elements. As a consequence for the 2-groups G and H of maximal class we have that V(𝔽₂ G) and V(𝔽₂ H) are isomorphic if and only if G and H are isomorphic.     

带性能约束布局问题的全局优化算法

以人造卫星仪器舱布局为例,应用图论,群对集合的作用,轨道与等价关系等刻划各种布局方案的同构,等价类等内在性质,从而首次给出带有性能约束二维布局问题的一个全局优化算法。     

HX环的存在性

自李洪兴１９９１年提出了ＨＸ环这一问题以来,一直有这么一个问题没有解决,即是否存在非平凡的ＨＸ环的例子？但至今既没有找到非平凡的ＨＸ环,也没有证明任一环Ｒ上仅存在平凡的ＨＸ环,钟育彬１９９５年证明了一类环上仅存在平凡的ＨＸ环,那么,是否所有环仅存在平凡的ＨＸ环呢？针对这一点,本文作进上步研究,构造了一个非平凡的ＨＸ环,并建立了ＨＸ环上的同态与同构定理,为进上步研究ＨＸ环奠定了基础。     

Non-associative algebras containing the matrix ring

The Lie admissible non-associative algebra is defined in the papers [Seul Hee Choi, Ki-Bong Nam, Derivations of a restricted Weyl type algebra I, Rocky Mountain J. Math. 37 (6) (2007) 1813–1830; Seul Hee Choi, Ki-Bong Nam, Weyl type non-associative algebra using additive groups I, Algebra Colloq. 14 (3) (2007) 479–488; Ki-Bong Nam, On Some Non-associative Algebras using Additive Groups, Southeast Asian Bull. Math., vol. 27, Springer-Verlag, 2003, 493–500]. We define in this work the algebra which generalizes the previous one and is not Lie admissible. We prove that the antisymmetrized Lie algebra is simple and contains the simple Lie algebra . We also prove that the matrix ring is embedded in .     

Derivations and isomorphisms of certain reflexive operator algebras

In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS) algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inne. We will also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial. Research supported by NSF of China and YSF of Shandong     

Isomorphism problems and groups of automorphisms for generalized Weyl algebras

We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities and the algebras similar to introduced by S. P. Smith. For the former, we generalize results of Dixmier on the first Weyl algebra and the minimal primitive factors of by finding sets of generators for the group of automorphisms.

     

Circulant digraphs determined by their spectra

Inspired by Ádám's conjecture the isomorphism problem of circulant digraphs is widely investigated. In the literature, the spectrum method was to solve the isomorphism problem for the circulants of prime-power order by some people. In this paper, we develop the spectrum method to characterize the circulant digraphs of orders p^a and p^aq^b, where p and q are distinct primes.     

Isomorphism classes of Doche–Icart–Kohel curves over finite fields

We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in two families of curves introduced by C. Doche, T. Icart and D.R. Kohel.