Heisenberg groups, semifields, and translation planes

2014 ◽  
Vol 56 (1) ◽  
pp. 115-127 ◽  
Author(s):  
Norbert Knarr ◽  
Markus J. Stroppel
Keyword(s):  
Translation Planes ◽  
Heisenberg Groups

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.

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

Translation planes admitting many homologies

1994 ◽  
Vol 49 (1-2) ◽  
pp. 117-149 ◽  
Author(s):  
Norman L. Johnson ◽  
Rolando Pomareda
Keyword(s):  
Translation Planes

scholarly journals Finite Heisenberg groups in quiver gauge theories

2006 ◽  
Vol 747 (3) ◽  
pp. 436-454 ◽  
Author(s):  
Benjamin A. Burrington ◽  
James T. Liu ◽  
Leopoldo A. Pando Zayas
Keyword(s):  
Gauge Theories ◽  
Heisenberg Groups
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