Publication result detail

Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity

HRDINA, J.; STODOLA, M.

Original Title

Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity

English Title

Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity

Type

WoS Article

Original Abstract

Using the classification of Clifford algebras and Bott periodicity, we show how higher geometric algebras can be realized as matrices over classical low dimensional geometric algebras. This matrix representation allows us to use standard geometric algebra software packages more easily. As an example, we express the geometric algebra for conics (GAC) as a matrix over the Compass ruler algebra (CRA).

English abstract

Using the classification of Clifford algebras and Bott periodicity, we show how higher geometric algebras can be realized as matrices over classical low dimensional geometric algebras. This matrix representation allows us to use standard geometric algebra software packages more easily. As an example, we express the geometric algebra for conics (GAC) as a matrix over the Compass ruler algebra (CRA).

Keywords

Conics;Geometric algebra;PGA;CGA;GAC;Witt pairs;Python

Key words in English

Conics;Geometric algebra;PGA;CGA;GAC;Witt pairs;Python

Authors

HRDINA, J.; STODOLA, M.

RIV year

2025

Released

31.08.2024

Publisher

Springer Nature

Location

BASEL 4052, SWITZERLAND

ISBN

0188-7009

Periodical

Advances in Applied Clifford Algebras

Volume

34

Number

4

State

Swiss Confederation

Pages from

1

Pages to

22

Pages count

22

URL

https://link.springer.com/article/10.1007/s00006-024-01346-7

Full text in the Digital Library

http://hdl.handle.net/11012/250095

BibTex

@article{BUT189563,
  author="Marek {Stodola} and Jaroslav {Hrdina}",
  title="Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity",
  journal="Advances in Applied Clifford Algebras",
  year="2024",
  volume="34",
  number="4",
  pages="1--22",
  doi="10.1007/s00006-024-01346-7",
  issn="0188-7009",
  url="https://link.springer.com/article/10.1007/s00006-024-01346-7"
}

Documents

s00006-024-01346-7