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IDEAL STRUCTURE OF CLIFFORD ALGEBRAS
, 902
"... Abstract. The structures of the ideals of Clifford algebras which can be both infinite dimensional and degenerate over the real numbers are investigated. 1. ..."
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Abstract. The structures of the ideals of Clifford algebras which can be both infinite dimensional and degenerate over the real numbers are investigated. 1.
ORTHOGONAL SYMMETRIES AND CLIFFORD ALGEBRAS
"... Abstract. Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries areinvestigated. ..."
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Cited by 3 (1 self)
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Abstract. Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries areinvestigated.
On hyperbolic Clifford algebras with involution ∗
, 2008
"... The aim of this article is to provide a characterization of quadratic forms of low dimension such that the canonical involutions of the their Clifford algebras are hyperbolic. 1 ..."
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The aim of this article is to provide a characterization of quadratic forms of low dimension such that the canonical involutions of the their Clifford algebras are hyperbolic. 1
Idempotents of Clifford Algebras ∗
, 2008
"... A classification of idempotents in Clifford algebras C p,q is presented. It is shown that using isomorphisms between Clifford algebras C p,q and appropriate matrix rings, it is possible to classify idempotents in any Clifford algebra into continuous families. These families include primitive idempot ..."
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A classification of idempotents in Clifford algebras C p,q is presented. It is shown that using isomorphisms between Clifford algebras C p,q and appropriate matrix rings, it is possible to classify idempotents in any Clifford algebra into continuous families. These families include primitive
Projective Geometry with Clifford algebra
 ACTA APPLICANDAE MATHEMATICAE
, 1991
"... Projective geometry is formulated in the language of geometric algebra, a unified mathematical language based on Clifford algebra. This closes the gap between algebraic and synthetic approaches to projective geometry and facilitates connections with the rest of mathematics. ..."
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Cited by 51 (9 self)
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Projective geometry is formulated in the language of geometric algebra, a unified mathematical language based on Clifford algebra. This closes the gap between algebraic and synthetic approaches to projective geometry and facilitates connections with the rest of mathematics.
On Computational Complexity of Clifford Algebra
, 2009
"... After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl(2m) that simplifies greatly the actual calculations and, without resorting to the conventional matrix isomorphism formulation, obtains the same complexity. In the last p ..."
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Cited by 3 (3 self)
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After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl(2m) that simplifies greatly the actual calculations and, without resorting to the conventional matrix isomorphism formulation, obtains the same complexity. In the last
Basic Calculations on Clifford Algebras
, 2008
"... Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2 with addition and multiplication being effectively computable r ..."
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Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2 with addition and multiplication being effectively computable
Expansions and Summations in Clifford Algebra
, 2002
"... Abstract. Clifford algebra is an important tool in theoretical physics, computational geometry and engineering applications, and coordinatefree computation is a salient feature of the geometric algebraic version of Clifford algebra. In this paper we establish some fundamental formulas on coordinat ..."
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Abstract. Clifford algebra is an important tool in theoretical physics, computational geometry and engineering applications, and coordinatefree computation is a salient feature of the geometric algebraic version of Clifford algebra. In this paper we establish some fundamental formulas
Clifford algebra with Mathematica
, 2008
"... The Clifford algebra of a ndimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, a package for Clifford algebra calculations for the computer algebra program Mathematica 1 is introdu ..."
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The Clifford algebra of a ndimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, a package for Clifford algebra calculations for the computer algebra program Mathematica 1
Results 1  10
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14,592