Quasilinear multiplication in the real Cayley–Dickson tower
Preprint CC BY · · arXiv:2609.11588
A quasilinear algorithm for multiplication of elements of Cayley–Dickson algebras with a tested and benchmarked MIT-licensed implementation.
Research
Papers & Preprints
Research Interests
Invariants and algebraic structure
Automorphisms, derivations, centers, nuclei, and subalgebra structure. How do these structures change with dimension, and which properties persist throughout the Cayley–Dickson tower?
Multiplication operators
Determinants, characteristic and minimal polynomials, ranks, kernels, and operator spectra. How do the determinants and characteristic polynomials of multiplication operators on An factor, and what do these factorizations reveal about the underlying algebra?
Arithmetic complexity and multiplication algorithms
Bilinear complexity, tensor rank, recursive multiplication, and arithmetic operation counts. What is the least number of scalar operations needed to multiply in An, and which algorithms attain or approach this bound?
Zero divisors, annihilators, and geometry
Zero-divisor families, annihilator dimensions, and the geometry of zero-divisor loci. How can zero divisors in An be classified through their annihilators, and what geometric structures organize these families?
Connections with other mathematical structures
Twisted group algebras, Clifford algebras, exceptional Lie groups, and projective geometry. Which structures associated with the classical division algebras extend to higher Cayley–Dickson algebras, and how do these relationships change along the tower?