Classification of sesquilinear forms, pairs of Hermitian forms, self-conjugate and isometric operators over the division ring of quaternions

1991 ◽  
Vol 49 (4) ◽  
pp. 409-414 ◽  
Author(s):  
V. V. Sergeichuk
Keyword(s):  
Division Ring ◽  
Sesquilinear Forms ◽  
Hermitian Forms

scholarly journals Classification of first order sesquilinear forms

2020 ◽  
Vol 32 (09) ◽  
pp. 2050027
Author(s):  
Matteo Capoferri ◽  
Nikolai Saveliev ◽  
Dmitri Vassiliev
Keyword(s):  
Dimensional Manifold ◽  
Sesquilinear Forms ◽  
Hermitian Forms ◽  
First Order ◽  
Gauge Equivalence ◽  
Lorentzian Metric ◽  
Sesquilinear Form ◽  
Special Case ◽  
Natural Way

A natural way to obtain a system of partial differential equations on a manifold is to vary a suitably defined sesquilinear form. The sesquilinear forms we study are Hermitian forms acting on sections of the trivial [Formula: see text]-bundle over a smooth [Formula: see text]-dimensional manifold without boundary. More specifically, we are concerned with first order sesquilinear forms, namely, those generating first order systems. Our goal is to classify such forms up to [Formula: see text] gauge equivalence. We achieve this classification in the special case of [Formula: see text] and [Formula: see text] by means of geometric and topological invariants (e.g., Lorentzian metric, spin/spinc structure, electromagnetic covector potential) naturally contained within the sesquilinear form — a purely analytic object. Essential to our approach is the interplay of techniques from analysis, geometry, and topology.

Classification of Hermitian Forms. VI Group Rings

1976 ◽  
Vol 103 (1) ◽  
pp. 1 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Group Rings ◽  
Hermitian Forms

On the classification of Hermitian forms

1972 ◽  
Vol 18 (1-2) ◽  
pp. 119-141 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Hermitian Forms

scholarly journals ENDOSCOPY AND COHOMOLOGY IN A TOWER OF CONGRUENCE MANIFOLDS FOR

2019 ◽  
Vol 7 ◽  
Author(s):  
SIMON MARSHALL ◽  
SUG WOO SHIN
Keyword(s):  
Symmetric Spaces ◽  
Unitary Groups ◽  
Automorphic Representations ◽  
Locally Symmetric Spaces ◽  
Hermitian Forms ◽  
Work In Progress ◽  
Endoscopic Classification

By assuming the endoscopic classification of automorphic representations on inner forms of unitary groups, which is currently work in progress by Kaletha, Minguez, Shin, and White, we bound the growth of cohomology in congruence towers of locally symmetric spaces associated to$U(n,1)$. In the case of lattices arising from Hermitian forms, we expect that the growth exponents we obtain are sharp in all degrees.

scholarly journals Topological classification of sesquilinear forms: Reduction to the nonsingular case

2016 ◽  
Vol 504 ◽  
pp. 581-589 ◽  
Author(s):  
Carlos M. da Fonseca ◽  
Tetiana Rybalkina ◽  
Vladimir V. Sergeichuk
Keyword(s):  
Topological Classification ◽  
Sesquilinear Forms

scholarly journals Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms

2008 ◽  
Vol 319 (6) ◽  
pp. 2351-2371 ◽  
Author(s):  
Vyacheslav Futorny ◽  
Roger A. Horn ◽  
Vladimir V. Sergeichuk
Keyword(s):  
Sesquilinear Forms ◽  
Hermitian Forms
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