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Dergiler / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

The Determinant Inner Product and the Heisenberg Product of Sym(2)

Mircea CRASMAREANU
Sayfa
145–146
Yayın Tarihi
2022-10-18
DOI
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Also, the product det is treated with complex numbers by using the Hopfinvariant map of Sym(2) and this complex approach yields a Heisenberg product on Sym(2).Moreover, the quadratic equation of critical points for a rational Morse function of height typegenerates a cosymplectic structure on Sym(2) with the unitary matrix as associated Reeb vector andwith the Reeb 1-form being half of the trace map.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The aim of this work is to introduce and study the nondegenerate inner product det inducedby the determinant map on the space Sym(2) of symmetric 2 2 real matrices.
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Temel Bulgular & Veri:This symmetricbilinear form of index 2 defines a rational symmetric function on the pairs of rays in the planeand an associated function on the 2-torus can be expressed with the usual Hopf bundle projectionS3 !
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Sonuç & Katkı:Also, the product det is treated with complex numbers by using the Hopfinvariant map of Sym(2) and this complex approach yields a Heisenberg product on Sym(2).Moreover, the quadratic equation of critical points for a rational Morse function of height typegenerates a cosymplectic structure on Sym(2) with the unitary matrix as associated Reeb vector andwith the Reeb 1-form being half of the trace map.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

The aim of this work is to introduce and study the nondegenerate inner product det inducedby the determinant map on the space Sym(2) of symmetric 2 2 real matrices. This symmetricbilinear form of index 2 defines a rational symmetric function on the pairs of rays in the planeand an associated function on the 2-torus can be expressed with the usual Hopf bundle projectionS3 ! S2( 12 ). Also, the product det is treated with complex numbers by using the Hopfinvariant map of Sym(2) and this complex approach yields a Heisenberg product on Sym(2).Moreover, the quadratic equation of critical points for a rational Morse function of height typegenerates a cosymplectic structure on Sym(2) with the unitary matrix as associated Reeb vector andwith the Reeb 1-form being half of the trace map.

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Bu Makaleye Atıf Yap

CRASMAREANU, M. (2022). The Determinant Inner Product and the Heisenberg Product of Sym(2). International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 145–146. https://ajindex.com/articles/539570

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