Heisenberg algebras, Heisenberg groups, Minkowski metrics, Jordan algebras and SL(2,ℂ)

2008 ◽  
pp. 107-130
Author(s):  
Ernst Binz ◽  
Sonja Pods
Keyword(s):  
Jordan Algebras ◽  
Heisenberg Groups ◽  
Heisenberg Algebras ◽  
Minkowski Metrics

scholarly journals Counting and equidistribution in quaternionic Heisenberg groups

2021 ◽  
pp. 1-38
Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN
Keyword(s):  
Hyperbolic Geometry ◽  
Quaternion Algebra ◽  
Rational Points ◽  
Hyperbolic Spaces ◽  
Heisenberg Groups ◽  
Arithmetic Groups ◽  
Hermitian Forms ◽  
Dimension 2 ◽  
Counting Formula ◽  
The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

Reducibly free nonspecial Jordan algebras

1989 ◽  
Vol 30 (1) ◽  
pp. 159-160 ◽  
Author(s):  
S. R. Sverchkov
Keyword(s):  
Jordan Algebras

scholarly journals Quantum Heisenberg groups and sklyanin algebras

1994 ◽  
Vol 31 (3) ◽  
pp. 167-177 ◽  
Author(s):  
Nicol�s Andruskiewitsch ◽  
Jorge Devoto ◽  
Alejandro Tiraboschi
Keyword(s):  
Heisenberg Groups ◽  
Sklyanin Algebras

Multiplicative-Semiprimeness of Nondegenerate Jordan Algebras

2004 ◽  
Vol 32 (10) ◽  
pp. 3995-4003 ◽  
Author(s):  
M. Cabrera ◽  
A. R. Villena
Keyword(s):  
Jordan Algebras
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