Simple Novikov Research Articles

On finite dimensional simple Novikov superalgebras

In this article, we prove that every finite dimensional simple Novikov superalgebra over a field of characteristic not equal 2 is trivial, i.e., .

Novikov–Poisson Algebras and Superalgebras of Jordan Brackets

We prove that for a generalized Novikov–Poisson algebra ⟨ A, ·, ○ ⟩ the bracket is a Jordan bracket, and therefore, the Kantor superalgebra J(A, {,}) is a Jordan superalgebra. Also we prove that ⟨ A, ○ ⟩ is nontrivial simple Novikov algebra and A = AA if and only if J(A, {,}) is a simple Jordan superalgebra.

Can a quantitative simulation of an Otto engine be accurately rendered by a simple Novikov model with heat leak?

In this case study a complex Otto engine simulation provides data including, but not limited to, effects from losses due to heat conduction, exhaust losses and frictional losses. This data is used as a benchmark to test whether the Novikov engine with heat leak, a simple endoreversible model, can reproduce the complex engine behavior quantitatively by an appropriate choice of model parameters. The reproduction obtained proves to be of high quality.

Some Results on Infinite Dimensional Novikov Algebras

This paper gives some sufficient conditions for determining the simplicity of infinite dimensional Novikov algebras of characteristic 0, and also constructs a class simple Novikov algebras by extending the base field. At last, the deformation theory of Novikov algebras is introduced.

Classification of Simple Novikov Algebras and Their Irreducible Modules of Characteristic 0

In this paper, we first present a classification theorem of simple infinite-dimensional Novikov algebras over an algebraically closed field of characteristic 0. Then we classify all the irreducible modules of certain infinite-dimensional simple Novikov algebras with an idempotent element whose left action is locally finite.

Quadratic Conformal Superalgebras

In this paper, we shall classify “quadratic” conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov superalgebra. Four general constructions of such pairs are given. Moreover, we shall classify such pairs related to simple Novikov algebras.

On nonsingular modules over infinite-dimensional simple novikov algebra of characteristic 0

In this paper we show that an A-module is a direct sum of a trivial module and a nosingular module, and we also give the structure of nonsingular module over infinite dimensional simple Novikov algebras of types (II) and (III) over a field F of Characteristic 0.

A Generalization of Rings of Type (1, 1)

x , y , z s x , z , y 1 Ž . Ž . Ž . Ž . w x Ž . have been studied. Among these are rings of type 1, 1 2 , which satisfy 1 Ž . Ž . w x and x, x, x s 0, third power associativity , Novikov rings 4, 6, 7, 10 , Ž . Ž . Ž . which satisfy 1 and x yz s y xz , and more recently rings which satisfy Ž . Ž w x . w x 1 and w, y, z , s s 0, 1, 8 . In the present paper we study rings Ž . Ž Ž . . Ž . satisfying 1 and w, x, x, x , y s 0. This generalizes rings of type 1, 1 . Ž w x . w 2 x Ž . It also generalizes the identity w, y, z , s s 0, since x , x s x, x, x . The result we obtain is that simple rings of characteristic / 2, 3, 5 must be associative. There exist examples of simple Novikov rings which are not w x associative 3 , and there exist examples of right alternative division rings Ž Ž .. w x of characteristic 2 thus of type 1, 1 which are not associative 9 .

A COMPLETE CLASSIFICATION OF FINITE-DIMENSIONAL SIMPLE NOVIKOV ALGEBRAS OF CHARACTERISTIC p > 2

Abstract In the paper we will give a complete classification of finite-dimensional simple Novikov algebras over an algebraically closed field with prime characteristic p > 2.

Novikov–Poisson Algebras

We classify Novikov–Poisson algebras whose Novikov algebras are simple with an idempotent element. Moreover, a class of simple Novikov algebras without idempotent elements is constructed through Novikov–Poisson algebras. Certain new simple Lie superalgebras induced by Novikov–Poisson algebras are introduced.

On Simple Novikov Algebras and Their Irreducible Modules

We give a complete classification of finite-dimensional simple Novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic. Moreover, we introduce “Novikov–Poisson algebras” and their tensor theory. Our tensor theory enables us to understand better certain finite-dimensional simple Novikov algebras and their irreducible modules.

Nonassociative algebras related to Hamiltonian operators in the formal calculus of variations

The main result in this paper is the classification of simple Novikov algebras A with a maximal subalgebra H such that A H has a finite-dimensional irreducible H -submodule. A second result deals with the extension of Hamiltonian operators.