Publication detail

Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity

HRDINA, J. STODOLA, M.

English title

Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity

Type

journal article in Web of Science

Language

en

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 in English

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

Released

31.08.2024

Publisher

SPRINGER BASEL AG

Location

BASEL 4052, SWITZERLAND

ISSN

0188-7009

Volume

34

Number

4

Pages from–to

1–22

Pages count

22

BIBTEX


@article{BUT189563,
  author="Jaroslav {Hrdina} and Marek {Stodola},
  title="Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity",
  year="2024",
  volume="34",
  number="4",
  month="August",
  pages="1--22",
  publisher="SPRINGER BASEL AG",
  address="BASEL 4052, SWITZERLAND",
  issn="0188-7009"
}