Cohomology of the Schrdinger Algebra S(1)

We explicitly compute the first and second cohomology groups of the Schrdinger algebra S(1) with coefficients in the trivial module and the finite-dimensional irreducible modules.We also show that the first and second cohomology groups of S(1) with coefficients in the universal enveloping algebras U(S(1))(under the adjoint action) are infinite dimensional.     

3-LIE BIALGEBRAS

3-Lie algebras have close relationships with many important fields in mathemat- ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char- acteristic zero are provided.     

Construction and classification of complex simple Lie algebras via projective geometry

We construct the complex simple Lie algebras using elementary algebraic geometry. We use our construction to obtain a new proof of the classification of complex simple Lie algebras that does not appeal to the classification of root systems.     

K-Theory of Stable Generalized Operator Algebras

It is proved that algebraic and topological K-functors are isomorphic on the category of stable generalized operator algebras which are K _i -regular for all i > 0.     

On multiplicities of simple subquotients in generalized Verma modules

We reduce the problem on multiplicities of simple subquotients in an -stratified generalized Verma module to the analogous problem for classical Verma modules.     

Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part

In this note we describe (up to isomorphism) the real von Neiman algebras R with Abelian skew-symmetric part , i.e., such that xy-yx=0 for any .     

THE SERRE RELATIONS IN RINGEL－HALL ALGEBRAS

The author constructs the Casimir element of Hall algebras.By the method of Gabber-Kactheorem(see [4]),it is proved that the Serre relations are the defining relations in compositionalgebra.     

Test Sets in Free Metabelian Lie Algebras

We calculate the test rank of a finite rank free metabelian Lie algebra over an arbitrary field and characterize the test sets for these algebras. We prove that each automorphism that is the identity modulo the derived subalgebra and that acts as the identity on some test set is an inner automorphism.     

Supporting disciplinary and interdisciplinary knowledge development and design thinking in an informal,pre‐engineering program: A Workplace Simulation Project

In this paper, we examined students’ engagement in an implementation of a Workplace Simulation Project (WSP). The WSP was designed to actively engage students in learning disciplinary content by inviting engineers from industry to have a physical presence within the school building to collaborate with teachers and students to complete projects which simulate the tasks authentic to their work. We focus on the first year implementation of the program that partnered a high school in the rural Midwest with an engineering unit of a government organization. Using a multiple methods study design, we analyzed disciplinary and interdisciplinary pre and posts test along with students’ interviews to determine learning gains as well as students’ interpretations of creative and critical thinking as experienced in the project and their knowledge of the engineering design process. Effect sizes showed that students in the WSP group had notable gains over the control group participants. Additionally, students’ knowledge of core elements of the design process were identified in inductive analyses of the interviews. Findings from this study will provide usable knowledge about effective ways to support systems and design thinking and ways to support expert‐novice collaboration to ensure success.     

Fractional supersymmetric su(2) algebras

In this paper, the third root of the Lie algebra su(2) based on the permutation group S₃ is formulated in the Hopf algebra formalism.