# Classification of generalized quantum statistics associated with the exceptional Lie (super)algebras

## Abstract

Generalized quantum statistics (GQS) associated with a Lie algebra or Lie superalgebra extends the notion of para-Bose or para-Fermi statistics. Such GQS have been classified for all classical simple Lie algebras and basic classical Lie superalgebras. In the current paper we finalize this classification for all exceptional Lie algebras and superalgebras. Since the definition of GQS is closely related to a certain Z grading of the Lie (super)algebra G, our classification reproduces some known Z gradings of exceptional Lie algebras. For exceptional Lie superalgebras such a classification of Z gradings has not been given before.

- Authors:

- Department of Applied Mathematics and Computer Science, University of Ghent, Krijgslaan 281-S9, B-9000 Gent (Belgium)

- Publication Date:

- OSTI Identifier:
- 20929686

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 4; Other Information: DOI: 10.1063/1.2712914; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; BOSONS; CLASSIFICATION; FERMI STATISTICS; FERMIONS; GRADED LIE GROUPS; QUANTUM MECHANICS; STATISTICS

### Citation Formats

```
Stoilova, N. I., and Jeugt, J. van der.
```*Classification of generalized quantum statistics associated with the exceptional Lie (super)algebras*. United States: N. p., 2007.
Web. doi:10.1063/1.2712914.

```
Stoilova, N. I., & Jeugt, J. van der.
```*Classification of generalized quantum statistics associated with the exceptional Lie (super)algebras*. United States. doi:10.1063/1.2712914.

```
Stoilova, N. I., and Jeugt, J. van der. Sun .
"Classification of generalized quantum statistics associated with the exceptional Lie (super)algebras". United States.
doi:10.1063/1.2712914.
```

```
@article{osti_20929686,
```

title = {Classification of generalized quantum statistics associated with the exceptional Lie (super)algebras},

author = {Stoilova, N. I. and Jeugt, J. van der},

abstractNote = {Generalized quantum statistics (GQS) associated with a Lie algebra or Lie superalgebra extends the notion of para-Bose or para-Fermi statistics. Such GQS have been classified for all classical simple Lie algebras and basic classical Lie superalgebras. In the current paper we finalize this classification for all exceptional Lie algebras and superalgebras. Since the definition of GQS is closely related to a certain Z grading of the Lie (super)algebra G, our classification reproduces some known Z gradings of exceptional Lie algebras. For exceptional Lie superalgebras such a classification of Z gradings has not been given before.},

doi = {10.1063/1.2712914},

journal = {Journal of Mathematical Physics},

number = 4,

volume = 48,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2712914

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