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...on|Michelsohn|1989|pp=96-97}}</ref> In fact, on a [[Spin manifold]], every Clifford module is obtained by twisting the spinor bundle.<ref>{{harvnb|Berline|Getz ...not be confused with a [[Clifford bundle]], which is a bundle of Clifford algebras. ...

...theory of [[quantum group]]s. The most important class of graded quadratic algebras is [[Koszul algebra]]s. ...t1=Alexander |last2=Positselski |first2=Leonid |year=2005 |title=Quadratic algebras |volume=37 |url=https://books.google.com/books?id=5_ZrCKU4NpAC&pg=PA6 |page ...

...pringer.com/10.1007/s00006-007-0026-y|journal=Advances in Applied Clifford Algebras|language=en|volume=17|issue=2|pages=245–258|doi=10.1007/s00006-007-0026-y|s ...

...ariety of [[group (mathematics)|groups]], consist of congruence-permutable algebras, but some, like the variety of [[lattice (order)|lattices]], have members t ...> permute.{{r|Bergman|p=122}} A [[variety (universal algebra)|variety]] of algebras <math>\mathcal{V}</math> is referred to as '''congruence-permutable''' when ...

...The study of functions with arguments from a Clifford algebra is called [[Clifford analysis]]. ...the [[holomorphic functional calculus]]. Hypercomplex analysis on Banach algebras is called [[functional analysis]]. ...

...}</math> [[spacetime algebra]] (STA), which can each be defined within sub-algebras of QGA. | journal = [[Advances in Applied Clifford Algebras]] ...

...rd algebra (GCA)|(orthogonal) Clifford algebra|Clifford algebra|symplectic Clifford algebra|Weyl algebra}} ...eld#Unital algebra|unital]] [[associative algebra]] that generalizes the [[Clifford algebra]], and goes back to the work of [[Hermann Weyl]],<ref>{{cite journa ...

| known_for = Research in Clifford algebras, relativistic wave equations, quantum mechanics, and relativity ...AMP from 1998&ndash;2000. He used to be deputy coordinator of the Clifford Algebras International Research Open Studies,<ref>[http://www.icca7.ups-tlse.fr/cair ...

...of order {{math|[[power of two|2]]^2''n''}} is defined as the [[Clifford algebra]] of {{math|2''n''}}-[[dimension (vector space)|dimensional]] [[pse ...as {{math|'''R'''^{''p'', ''q''}}} and their respective geometric algebras {{math|<math>\mathcal{G}</math>(''p'', ''q'')}}. ...

''Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra, second edition,'' ...C., Dorst L. and [[Joan Lasenby|Lasenby J.]] (eds.) ''Applied Geometrical Algebras in computer Science and Engineering AGACSE 2001'', Birkhauser, Basel. ...

{{short description|Unital algebra homomorphism of exterior algebras}} ...is, an outermorphism is a unital [[algebra homomorphism]] between exterior algebras. ...

''Clifford structures'' are fundamental in studying Osserman manifolds. An [[Riemann c ...o does. These structures naturally arise from unitary representations of [[Clifford algebra]]s and provide a way to construct examples of Osserman manifolds. T ...

...|page=100 |author=William E Baylis |title=Lectures on Clifford (geometric) algebras and applications |isbn=0-8176-3257-3 |year=2004 |chapter=§4.2.3 Higher-grad * [[Clifford algebra]] ...

...ord analysis''', using [[Clifford algebra]]s named after [[William Kingdon Clifford]], is the study of [[Dirac operator]]s, and Dirac type operators in analysi ...>, and '''R'''^''n'' is considered to be embedded in a complex [[Clifford algebra]], Cl_''n''('''C''') so that {{nowrap|1=''e''<sub>''j''</ ...

...gations of ''Spaces over Algebras''.<ref>A.P. Shirokov (2002) "Spaces over algebras and their applications", ''Journal of Mathematical Sciences'' 108(2): 232–4 ...ional algebra of doubled [[quaternion]]s <math>\mathbb{H}</math> was used. Clifford had shown that a space of rotations entailed [[Elliptic geometry|elliptic s ...

...f conformal orthogonal group elements |journal=Clifford Analysis, Clifford Algebras and Their Applications |volume=4 |pages=223–240 |url=https://spark.siue.edu ...

...author2=Roldão da Rocha, Jr. |year=2016 |title=An Introduction to Clifford Algebras and Spinors |publisher=[[Oxford University Press]] |page=140 |isbn=97801910 ...orm]].{{refn|{{citation |author=Ian R. Porteous |year=1995 |title=Clifford Algebras and the Classical Groups |publisher=[[Cambridge University Press]] }}}} ...

...was first introduced as a [[combinatorial]] object by [[Raoul Bott]] and [[Clifford Taubes]]<ref name="Bott Taubes">{{cite journal | first2=Clifford ...

{{Short description|Gamma matrices for arbitrary Clifford algebras}} ...y the basis elements <math>e_a</math> (ignoring the additive aspect of the Clifford algebra). ...

...ge, G. Martens: [http://www.numdam.org/article/CM_1989__72_2_173_0.pdf The Clifford dimension of a projective curve], Compositio Math., vol. 72, 1989, pp., 173 *with David Eisenbud: Sheaf Cohomology and Free Resolutions over Exterior Algebras, [https://arxiv.org/abs/math/0005055 Arxiv 2000] ...