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pro vyhledávání: '"15A66"'
In this paper we use the power of the outer exponential $\Lambda^B$ of a bivector $B$ to see the so-called invariant decomposition from a different perspective. This is deeply connected with the eigenvalues for the adjoint action of $B$, a fact that
Externí odkaz:
http://arxiv.org/abs/2412.20566
Autor:
Sharma, Heerak, Shirokov, Dmitry
The generators of a Clifford algebra anti-commute. This anti-commutativity is essential and allows the algebra to describe the plethora of things it is able to describe. It is then a natural question whether an analogous algebra whose generators comm
Externí odkaz:
http://arxiv.org/abs/2412.20135
Autor:
Acus, A., Dargys, A.
The modern algebra concepts are used to construct tables of algebraic spinors related to Clifford algebra multivectors with real and complex coefficients. The following data computed by Mathematica are presented in form of tables for individual Cliff
Externí odkaz:
http://arxiv.org/abs/2412.14677
Autor:
Mathews, Daniel V., Varsha
We give explicit bijective correspondences between three families of objects: certain pairs of quaternions, which we regard as spinors; certain flags in (1+4)-dimensional Minkowski space; and horospheres in 4-dimensional hyperbolic space decorated wi
Externí odkaz:
http://arxiv.org/abs/2412.06572
Autor:
Acus, A., Dargys, A.
Explicit formulas to calculate MV functions in a basis-free representation are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on analysis of the roots of minimal MV polynomial and covers defective MVs, i.e. the
Externí odkaz:
http://arxiv.org/abs/2412.05730
Autor:
Shirokov, D. S.
In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in the case of
Externí odkaz:
http://arxiv.org/abs/2412.02772
Autor:
Shirokov, D. S.
We introduce the notion of rank of multivector in Clifford geometric algebras of arbitrary dimension without using the corresponding matrix representations and using only geometric algebra operations. We use the concepts of characteristic polynomial
Externí odkaz:
http://arxiv.org/abs/2412.02681
In the complete hyperbolic structure on the complement of the figure eight knot, we determine the set of lambda lengths from the maximal cusp to itself. Using the correspondence between spinors and spin-decorated horospheres, we show that these lambd
Externí odkaz:
http://arxiv.org/abs/2411.06368
The dual Drazin inverse is an important dual generalized inverse. In this paper, to extend it we introduce the weak dual Drazin inverse which is unique and exists for any square dual matrix. When the dual Drazin inverse exists, it coincides with the
Externí odkaz:
http://arxiv.org/abs/2411.06328
Autor:
Rumyantseva, S. V., Shirokov, D. S.
It is easier to investigate phenomena in particle physics geometrically by exploring a real solution to the Dirac-Hestenes equation instead of a complex solution to the Dirac equation. The present research outlines the multidimensional Dirac-Hestenes
Externí odkaz:
http://arxiv.org/abs/2411.04214