Publication result detail

Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

HRDINA, J.; NÁVRAT, A.; VAŠÍK, P.; DORST, L.

Original Title

Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

English Title

Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

Type

WoS Article

Original Abstract

We show that if Projective Geometric Algebra (PGA), i.e. the geometric algebra with degenerate signature (n, 0, 1), is understood as a subalgebra of Conformal Geometric Algebra (CGA) in a mathematically correct sense, then flat primitives share the same representation in PGA and CGA. Particularly, we treat duality in PGA in the framework of CGA. This leads to unification of PGA and CGA primitives which is important especially for software implementation and symbolic calculations.

English abstract

We show that if Projective Geometric Algebra (PGA), i.e. the geometric algebra with degenerate signature (n, 0, 1), is understood as a subalgebra of Conformal Geometric Algebra (CGA) in a mathematically correct sense, then flat primitives share the same representation in PGA and CGA. Particularly, we treat duality in PGA in the framework of CGA. This leads to unification of PGA and CGA primitives which is important especially for software implementation and symbolic calculations.

Keywords

Conformal geometric algebra; Projective geometric algebra; Euclidean geometry

Key words in English

Conformal geometric algebra; Projective geometric algebra; Euclidean geometry

Authors

HRDINA, J.; NÁVRAT, A.; VAŠÍK, P.; DORST, L.

RIV year

2021

Released

22.02.2021

Publisher

Birkhauser Verlag AG

Location

Basel, Switzerland

ISBN

0188-7009

Periodical

Advances in Applied Clifford Algebras

Volume

31

Number

18

State

Swiss Confederation

Pages from

1

Pages to

13

Pages count

14

URL

https://link.springer.com/article/10.1007/s00006-021-01118-7

BibTex

@article{BUT169707,
  author="Jaroslav {Hrdina} and Aleš {Návrat} and Petr {Vašík} and Leo {Dorst}",
  title="Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra",
  journal="Advances in Applied Clifford Algebras",
  year="2021",
  volume="31",
  number="18",
  pages="1--13",
  doi="10.1007/s00006-021-01118-7",
  issn="0188-7009",
  url="https://link.springer.com/article/10.1007/s00006-021-01118-7"
}