Olivier Elchinger - Profile on Academia.edu (original) (raw)

Mohamed Elhamdadi related author profile picture

Abdenacer Makhlouf related author profile picture

Sergei Silvestrov related author profile picture

Giacomo Graziani related author profile picture

Joseph Fourier related author profile picture

Lily Sullivan related author profile picture

Pavel Enriquez related author profile picture

Margaret Beattie related author profile picture

Alexander A Voronov related author profile picture

G. Militaru related author profile picture

Uploads

Papers by Olivier Elchinger

Research paper thumbnail of Twisting Poisson algebras, coPoisson algebras and Quantization

The purpose of this paper is to study twistings of Poisson algebras or bialgebras, coPoisson alge... more The purpose of this paper is to study twistings of Poisson algebras or bialgebras, coPoisson algebras or bialgebras and star-products. We consider Hom-algebraic structures generalizing classical algebraic structures by twisting the identities by a linear self map. We summarize the results on Hom-Poisson algebras and introduce Hom-coPoisson algebras and bialgebras. We show that there exists a duality between Hom-Poisson bialgebras and Hom-coPoisson bialgebras. A relationship between enveloping Homalgebras endowed with Hom-coPoisson structures and corresponding Hom-Lie bialgebra structures is studied. Moreover we set quantization problems and generalize the notion of star-product. In particular, we characterize the twists for the Moyal-Weyl product for polynomials of several variables.

Research paper thumbnail of Brackets with <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mtext> </mtext><mi>t</mi><mi>a</mi><mi>u</mi><mo separator="true">,</mo><mtext> </mtext><mi>s</mi><mi>i</mi><mi>g</mi><mi>m</mi><mi>a</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\ tau,\ sigma) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mspace"> </span><span class="mord mathnormal">t</span><span class="mord mathnormal">a</span><span class="mord mathnormal">u</span><span class="mpunct">,</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">ma</span><span class="mclose">)</span></span></span></span>-derivations and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>p</mi><mo separator="true">,</mo><mi>q</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(p, q) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">p</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mclose">)</span></span></span></span>-deformations of Witt and Virasoro algebras

The aim of this paper is to study some brackets defined on (τ, σ )-derivations satisfying quasi-L... more The aim of this paper is to study some brackets defined on (τ, σ )-derivations satisfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well as sl(2) algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on σ -derivations, arising in connection with discretizations and deformations of algebras of vector fields.

Research paper thumbnail of Twisting Poisson algebras, coPoisson algebras and Quantization

The purpose of this paper is to study twistings of Poisson algebras or bialgebras, coPoisson alge... more The purpose of this paper is to study twistings of Poisson algebras or bialgebras, coPoisson algebras or bialgebras and star-products. We consider Hom-algebraic structures generalizing classical algebraic structures by twisting the identities by a linear self map. We summarize the results on Hom-Poisson algebras and introduce Hom-coPoisson algebras and bialgebras. We show that there exists a duality between Hom-Poisson bialgebras and Hom-coPoisson bialgebras. A relationship between enveloping Homalgebras endowed with Hom-coPoisson structures and corresponding Hom-Lie bialgebra structures is studied. Moreover we set quantization problems and generalize the notion of star-product. In particular, we characterize the twists for the Moyal-Weyl product for polynomials of several variables.

Research paper thumbnail of Brackets with <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mtext> </mtext><mi>t</mi><mi>a</mi><mi>u</mi><mo separator="true">,</mo><mtext> </mtext><mi>s</mi><mi>i</mi><mi>g</mi><mi>m</mi><mi>a</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\ tau,\ sigma) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mspace"> </span><span class="mord mathnormal">t</span><span class="mord mathnormal">a</span><span class="mord mathnormal">u</span><span class="mpunct">,</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">ma</span><span class="mclose">)</span></span></span></span>-derivations and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>p</mi><mo separator="true">,</mo><mi>q</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(p, q) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">p</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mclose">)</span></span></span></span>-deformations of Witt and Virasoro algebras

The aim of this paper is to study some brackets defined on (τ, σ )-derivations satisfying quasi-L... more The aim of this paper is to study some brackets defined on (τ, σ )-derivations satisfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well as sl(2) algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on σ -derivations, arising in connection with discretizations and deformations of algebras of vector fields.

Log In