Generalizes projective cross-ratios to every grade of geometric object in n-dimensional PGA with explicit formulas, duality pairs, and recovery of classical invariants.
Clifford algebra, geometric algebra, and applications
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abstract
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra construction (then called geometric algebra) with geometric applications in mind, as well as in an algebraically more general form which is well suited for combinatorics, and for defining and understanding the numerous products and operations of the algebra. The various applications presented include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
The Ising transfer matrix and its excitations are re-expressed as elements of a conformal Clifford algebra, with the eigenvalue problem becoming a dispersion relation for free Majorana quasiparticles.
citing papers explorer
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Generalize cross-ratios in n-dimensional Plane-Based Geometric Algebra
Generalizes projective cross-ratios to every grade of geometric object in n-dimensional PGA with explicit formulas, duality pairs, and recovery of classical invariants.
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On the geometric algebras of the Ising model
The Ising transfer matrix and its excitations are re-expressed as elements of a conformal Clifford algebra, with the eigenvalue problem becoming a dispersion relation for free Majorana quasiparticles.