# Octonion, pseudo-alternative, and Lie-admissible algebras

## Abstract

It has been shown that any octonion algebra can always be derivable from some pseudo-alternative algebra. As examples, both Cayley-Dickson process and Zorn's vector matrix algebra as well as their generalizations have been re-written as pseudo-alternative algebras. Also, an analogue of Cayley-Dickson process for Lie-admissible algebra has been proposed.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Rochester, NY

- OSTI Identifier:
- 6789226

- Alternate Identifier(s):
- OSTI ID: 6789226

- DOE Contract Number:
- AC02-76ER13065

- Resource Type:
- Journal Article

- Journal Name:
- Hadronic J.; (United States)

- Additional Journal Information:
- Journal Volume: 2:1

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LIE GROUPS; ALGEBRA; MATHEMATICS; SYMMETRY GROUPS 658000* -- Mathematical Physics-- (-1987)

### Citation Formats

```
Okubo, S.
```*Octonion, pseudo-alternative, and Lie-admissible algebras*. United States: N. p., 1979.
Web.

```
Okubo, S.
```*Octonion, pseudo-alternative, and Lie-admissible algebras*. United States.

```
Okubo, S. Thu .
"Octonion, pseudo-alternative, and Lie-admissible algebras". United States.
```

```
@article{osti_6789226,
```

title = {Octonion, pseudo-alternative, and Lie-admissible algebras},

author = {Okubo, S.},

abstractNote = {It has been shown that any octonion algebra can always be derivable from some pseudo-alternative algebra. As examples, both Cayley-Dickson process and Zorn's vector matrix algebra as well as their generalizations have been re-written as pseudo-alternative algebras. Also, an analogue of Cayley-Dickson process for Lie-admissible algebra has been proposed.},

doi = {},

journal = {Hadronic J.; (United States)},

number = ,

volume = 2:1,

place = {United States},

year = {1979},

month = {2}

}

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