Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
TERNARY ALGEBRAIC CONSTRUCTION OF EXTENDED SUPERCONFORMAL ALGEBRAS
View through CrossRef
We give a construction of extended (N = 2 and N = 4) superconformal algebras over a very general class of ternary algebras (triple systems). For N = 2 this construction leads to superconformal algebras corresponding to certain coset spaces of Lie groups with non-vanishing torsion and generalizes a previous construction over Jordan triple systems which are associated with Hermitian symmetric spaces. In general, a given Lie group admits more than one coset space of this type. We give examples for all simple Lie groups. In particular, the division algebras and their tensor products lead to N = 2 superconformal algebras associated with the groups of the Magic Square. For a very special class of ternary algebras, namely the Freudenthal triple (FT) systems, the N = 2 superconformal algebras can be extended to N = 4 superconformal algebras with the gauge group SU (2) × SU (2) × U (1). We give a complete list of the FT systems and the corresponding N = 4 models. They are associated with the unique quaternionic symmetric spaces of Lie groups.
Title: TERNARY ALGEBRAIC CONSTRUCTION OF EXTENDED SUPERCONFORMAL ALGEBRAS
Description:
We give a construction of extended (N = 2 and N = 4) superconformal algebras over a very general class of ternary algebras (triple systems).
For N = 2 this construction leads to superconformal algebras corresponding to certain coset spaces of Lie groups with non-vanishing torsion and generalizes a previous construction over Jordan triple systems which are associated with Hermitian symmetric spaces.
In general, a given Lie group admits more than one coset space of this type.
We give examples for all simple Lie groups.
In particular, the division algebras and their tensor products lead to N = 2 superconformal algebras associated with the groups of the Magic Square.
For a very special class of ternary algebras, namely the Freudenthal triple (FT) systems, the N = 2 superconformal algebras can be extended to N = 4 superconformal algebras with the gauge group SU (2) × SU (2) × U (1).
We give a complete list of the FT systems and the corresponding N = 4 models.
They are associated with the unique quaternionic symmetric spaces of Lie groups.
Related Results
Associative Ternary Algebras and Ternary Lie Algebras at Cube Roots of Unity
Associative Ternary Algebras and Ternary Lie Algebras at Cube Roots of Unity
We propose an approach to extending the concept of a Lie algebra to ternary structures based on ω-symmetry, where ω is a primitive cube root of unity. We give a definition of a cor...
Associative Ternary Algebras and Ternary Lie Algebras at Cube Roots of Unity
Associative Ternary Algebras and Ternary Lie Algebras at Cube Roots of Unity
We propose an approach to extend the concept of a Lie algebra to ternary structures based on ω-symmetry, where ω is a primitive cube root of unity. We give a definition of a corres...
Differential graded vertex Lie algebras
Differential graded vertex Lie algebras
This is the continuation of the study of differential graded (dg) vertex algebras defined in our previous paper [Caradot et al., “Differential graded vertex operator algebras and t...
Editorial Messages
Editorial Messages
Just as it has been continually happening in the world of mathematical sciences, the group of mathematical scientists led by (for example) Professor Eyup Cetin and his colleagues (...
Quantum B-algebras
Quantum B-algebras
Abstract
The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic...
Relations between L-algebras and other logical algebras
Relations between L-algebras and other logical algebras
In this paper, by considering the notion of L-algebra, we show that there are relations between L-algebras and some of other logical algebras such as residuated lattices, MTL-alge...
Finitely Presented Heyting Algebras
Finitely Presented Heyting Algebras
In this paper we study the structure of finitely presented Heyting<br />algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every s...
On Kreb Algebras
On Kreb Algebras
In this paper, kreb algebras are introduced. It is shown that that the class of kreb algebras is a wider class than the class of BCI algebras. Properties of kreb algebras are prese...