We look at two examples of homotopy Lie algebras (also known as L∞ algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators ∆ to verify the homotopy Lie data is shown to produce the sa...

We look at two examples of homotopy Lie algebras (also known as L∞ algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators ∆ to verify the homotopy Lie data is shown to produce the sa...

Abstract Let p be a prime and let G finite group such that the smallest divides | is . We find sharp bounds, depending on , for commuting probability average character degree to guarantee nilpotent or supersolvable.

We review the detailed structure of the large N = 4 superconformal algebra, and construct its BRST operator which constitutes the main object for analyzing N = 4 strings. We then derive the general condition for the nilpotency of the BRST operator and show that there exists a line of critical N = 4 string theories. e-mail address: [email protected] e-mail address: [email protected], ohta@...

In this paper, we study the tensor commutativity degree of pair of finite groups. Erdos introduced the relative commutativity degree and studied its properties. Then, Mr. Niroomand introduced the tensor relative commutativity degree, calculated tensor relative degree for some groups, and studied its properties. Also, he explained its relation with relative commutativity degree. In this paper, w...

In this paper are determined minimal shape-preserving projections onto the n-th degree algebraic polynomials.

There are many methods to solve equation of degree n with one unknown, but the restrictions most very harsh. Based on Vieta’s theorem, this paper gives symbolic effective coefficient method and elimination rotation symmetry n-th variable.