Cliffordn.

Brit.

/ˈklɪfəd/, U.S.

/ˈklɪfərd/

Origin: From a proper name. Etymon: proper name Clifford.

Etymology: < the name of William Kingdon Clifford (1845–79), English mathematician.

attributive. Designating mathematical concepts and structures devised by William Kingdon Clifford or arising out of his work.

1. Clifford algebra n. an associative algebra of a kind first described by Clifford in 1878 and subsequently used widely in physics, esp. in connection with the mathematical description of rotation.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > branch or subset of

quadratic1674

tactic1861

linear algebra1870

group theory1888

subalgebra1903

Clifford algebra1907

1907 J. B. Shaw Synopsis Linear Associative Algebra ii. xvi. 84 The Clifford algebra of order 2^m = 4^m′ is the product of m′ quaternion algebras.

1948 Ann. Math. 49 762 The above special construction proves the existence of a Clifford algebra of odd index whose fundamental terms are linearly dependent.

2011 D. J. H. Garling Clifford Algebras Introd. 3. Every Clifford algebra is either isomorphic to a full matrix algebra over R, C or H, or is isomorphic to the direct sum of two copies of one of these.

2. Clifford module n. a representation (representation n.¹ 5) of a Clifford algebra, regarded as a module (module n. 5b).

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > in abstract algebra > groups > quality

order1878

representation1897

realization1954

Clifford module1964

1964 M. F. Atiyah et al. in Topology 3 Suppl. 1, 3 We study Clifford modules, i.e. representations of the Clifford algebras.

1986 Proc. National Acad. Sci. U.S.A. 83 8442/2 The space..has a structure of a Clifford module over C.

2013 E. Meinrenken Clifford Algebras & Lie Theory iii. 65 The evaluation map defines an isomorphism of Clifford modules.

3. Clifford semigroup n. a semigroup all of whose elements belong to groups (group n. 7) contained by the semigroup; esp. such a semigroup having the further property that each of its elements has a unique inverse which is also contained in the semigroup.

ΚΠ

1964 Bull. Amer. Math. Soc. 70 766 A Clifford semigroup is a semigroup which is a union of groups.

1995 P. A. Grillet Semigroups iii. 75 Clifford semigroups are also called unions of groups and completely regular semigroups.

2011 U. Knauer Algebraic Graph Theory xiii. 279 After excluding many Clifford semigroups which cannot be planar, we now turn to positive cases.

This is a new entry (OED Third Edition, December 2016; most recently modified version published online March 2022).

单词	clifford
释义	Cliffordn. Brit. /ˈklɪfəd/, U.S. /ˈklɪfərd/ Origin: From a proper name. Etymon: proper name Clifford. Etymology: < the name of William Kingdon Clifford (1845–79), English mathematician. attributive. Designating mathematical concepts and structures devised by William Kingdon Clifford or arising out of his work. 1. Clifford algebra n. an associative algebra of a kind first described by Clifford in 1878 and subsequently used widely in physics, esp. in connection with the mathematical description of rotation. ΘΚΠ the world > relative properties > number > algebra > [noun] > branch or subset of quadratic1674 tactic1861 linear algebra1870 group theory1888 subalgebra1903 Clifford algebra1907 1907 J. B. Shaw Synopsis Linear Associative Algebra ii. xvi. 84 The Clifford algebra of order 2^m = 4^m′ is the product of m′ quaternion algebras. 1948 Ann. Math. 49 762 The above special construction proves the existence of a Clifford algebra of odd index whose fundamental terms are linearly dependent. 2011 D. J. H. Garling Clifford Algebras Introd. 3. Every Clifford algebra is either isomorphic to a full matrix algebra over R, C or H, or is isomorphic to the direct sum of two copies of one of these. 2. Clifford module n. a representation (representation n.¹ 5) of a Clifford algebra, regarded as a module (module n. 5b). ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > in abstract algebra > groups > quality order1878 representation1897 realization1954 Clifford module1964 1964 M. F. Atiyah et al. in Topology 3 Suppl. 1, 3 We study Clifford modules, i.e. representations of the Clifford algebras. 1986 Proc. National Acad. Sci. U.S.A. 83 8442/2 The space..has a structure of a Clifford module over C. 2013 E. Meinrenken Clifford Algebras & Lie Theory iii. 65 The evaluation map defines an isomorphism of Clifford modules. 3. Clifford semigroup n. a semigroup all of whose elements belong to groups (group n. 7) contained by the semigroup; esp. such a semigroup having the further property that each of its elements has a unique inverse which is also contained in the semigroup. ΚΠ 1964 Bull. Amer. Math. Soc. 70 766 A Clifford semigroup is a semigroup which is a union of groups. 1995 P. A. Grillet Semigroups iii. 75 Clifford semigroups are also called unions of groups and completely regular semigroups. 2011 U. Knauer Algebraic Graph Theory xiii. 279 After excluding many Clifford semigroups which cannot be planar, we now turn to positive cases. This is a new entry (OED Third Edition, December 2016; most recently modified version published online March 2022). < n.1907
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