Möbius Tramsformations and Clifford Algebras of Euclidean and Anti-Euclidean Spaces

1989 ◽  
pp. 79-90 ◽  
Author(s):  
Pertti Lounesto ◽  
Arthur Springer
Keyword(s):  
Clifford Algebras ◽  
Euclidean Spaces

scholarly journals Chirality of Dirac Spinors Revisited

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 616
Author(s):  
Michel Petitjean
Keyword(s):  
Group Theory ◽  
Clifford Algebras ◽  
Euclidean Spaces ◽  
Dirac Algebra ◽  
Mathematical Definition ◽  
Higher Dimensional ◽  
Symmetry Operators ◽  
Definition Of ◽  
Dirac Spinors

We emphasize the differences between the chirality concept applied to relativistic fermions and the ususal chirality concept in Euclidean spaces. We introduce the gamma groups and we use them to classify as direct or indirect the symmetry operators encountered in the context of Dirac algebra. Then we show how a recent general mathematical definition of chirality unifies the chirality concepts and resolve conflicting conclusions about symmetry operators, and particularly about the so-called chirality operator. The proofs are based on group theory rather than on Clifford algebras. The results are independent on the representations of Dirac gamma matrices, and stand for higher dimensional ones.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

Isomorphisms of graded skew Clifford algebras

2020 ◽  
Vol 13 (5) ◽  
pp. 871-878
Author(s):  
Richard G. Chandler ◽  
Nicholas Engel
Keyword(s):  
Clifford Algebras

On Riemann problems for monogenic functions in lower dimensional non-commutative Clifford algebras

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Carlos Daniel Tamayo-Castro ◽  
Ricardo Abreu-Blaya ◽  
Juan Bory-Reyes
Keyword(s):  
Clifford Algebras ◽  
Monogenic Functions ◽  
Riemann Problems ◽  
Lower Dimensional

scholarly journals Ancient solutions for Andrews’ hypersurface flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Peng Lu ◽  
Jiuru Zhou
Keyword(s):  
Ricci Flow ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Euclidean Spaces ◽  
Round Cylinder ◽  
Ancient Solutions ◽  
Singular Time

AbstractWe construct the ancient solutions of the hypersurface flows in Euclidean spaces studied by B. Andrews in 1994.As time {t\rightarrow 0^{-}} the solutions collapse to a round point where 0 is the singular time. But as {t\rightarrow-\infty} the solutions become more and more oval. Near the center the appropriately-rescaled pointed Cheeger–Gromov limits are round cylinder solutions {S^{J}\times\mathbb{R}^{n-J}}, {1\leq J\leq n-1}. These results are the analog of the corresponding results in Ricci flow ({J=n-1}) and mean curvature flow.

scholarly journals Equiangular lines in Euclidean spaces

2016 ◽  
Vol 138 ◽  
pp. 208-235 ◽  
Author(s):  
Gary Greaves ◽  
Jacobus H. Koolen ◽  
Akihiro Munemasa ◽  
Ferenc Szöllősi
Keyword(s):  
Euclidean Spaces ◽  
Equiangular Lines
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