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$𝒟$ -bundles and integrable hierarchies

David Ben-Zvi, Thomas Nevins (2011)

Journal of the European Mathematical Society

We study the geometry of $𝒟$ -bundles—locally projective $𝒟$ -modules—on algebraic curves, and apply them to the study of integrable hierarchies, specifically the multicomponent Kadomtsev–Petviashvili (KP) and spin Calogero–Moser (CM) hierarchies. We show that KP hierarchies have a geometric description as flows on moduli spaces of $𝒟$ -bundles; in particular, we prove that the local structure of $𝒟$ -bundles is captured by the full Sato Grassmannian. The rational, trigonometric, and elliptic solutions of KP...

$ℤ$ -graded Lie superalgebras of infinite depth and finite growth

Nicoletta Cantarini (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In 1998 Victor Kac classified infinite-dimensional $ℤ$ -graded Lie superalgebras of finite depth. We construct new examples of infinite-dimensional Lie superalgebras with a $ℤ$ -gradation of infinite depth and finite growth and classify $ℤ$ -graded Lie superalgebras of infinite depth and finite growth under suitable hypotheses.

$(H, R)$ -Lie coalgebras and $(H, R)$ -Lie bialgebras.

Zhang, Liangyun (2006)

Sibirskij Matematicheskij Zhurnal

$\mathcal{L}$ -homomorphisms of Lie algebras

Aleksander A. Lashkhi (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studiano gli omomorfismi reticolari ( $\mathcal{L}$ -omomorfismi) di algebre di Lie sopra anelli commutativi con unità. Le algebre di Lie sopra un campo e le $p$ -algebre di Lie non ammettono $\mathcal{L}$ -omomorfismi propri. Si assegnano condizioni necessarie e sufficienti affinchè un'algebra di Lie periodica o mista possieda un « $\mathcal{L}$ -omomorfismo su una catena di lunghezza $n$ .

$*$ -дифференцирования первичных алгебр Ли.

В.Т. Филиппов (1999)

Sibirskij matematiceskij zurnal

$1$ -cocycles on the group of contactomorphisms on the supercircle $S^{1 | 3}$ generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

The relative cohomology $H_{diff}^{1} (𝕂 (1 | 3), 𝔬𝔰𝔭 (2, 3); 𝒟_{λ, μ} (S^{1 | 3}))$ of the contact Lie superalgebra $𝕂 (1 | 3)$ with coefficients in the space of differential operators $𝒟_{λ, μ} (S^{1 | 3})$ acting on tensor densities on $S^{1 | 3}$ , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating $1$ -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative $1$ -cocycle $s (X_{f}) = D_{1} D_{2} D_{3} (f) α_{3}^{1 / 2}$ , $X_{f} \in 𝕂 (1 | 3)$ which is invariant with respect to the conformal subsuperalgebra $𝔬𝔰𝔭 (2, 3)$ of $𝕂 (1 | 3)$ . In this work we study the supergroup case. We give an explicit construction of $1$ -cocycles of the group...

3-filiform Lie algebras of dimension 8

L.M. Camacho, J.R. Gómez, R.M. Navarro (1999)

Annales mathématiques Blaise Pascal

(Finite) presentations of the Albert-Frank-Shalev Lie algebras

Claretta Carrara (2001)

Bollettino dell'Unione Matematica Italiana

In questo lavoro vengono studiate le algebre di Albert-Frank-Shalev. Queste sono algebre di Lie modulari di dimensione infinita, ottenute da un loop di certe algebre semplici di dimensione finita. Si dimostra che le algebre di Albert-Frank-Shalev sono unicamente determinate, a meno di elementi centrali o secondo centrali, da un certo quoziente finito-dimensionale. Tale risultato si ottiene dando la presentazione finita di un'algebra il cui quoziente sul secondo centro (infinito-dimensionale) è isomorfo...

Currently displaying 1 – 20 of 276

Page 1 Next

Displaying 1 – 20 of 276

$𝒟$ -bundles and integrable hierarchies

$ℤ$ -graded Lie superalgebras of infinite depth and finite growth

$(H, R)$ -Lie coalgebras and $(H, R)$ -Lie bialgebras.

$\mathcal{L}$ -homomorphisms of Lie algebras

$*$ -дифференцирования первичных алгебр Ли.

$1$ -cocycles on the group of contactomorphisms on the supercircle $S^{1 | 3}$ generalizing the Schwarzian derivative

3-filiform Lie algebras of dimension 8

(Finite) presentations of the Albert-Frank-Shalev Lie algebras

$𝔫$ -coinvariants des $𝔤$ -modules $𝔫$ -localement nilpotents

$𝔰𝔩 (2)$ -trivial deformations of ${Vect}_{Pol} (ℝ)$ -modules of symbols.

[unknown]

[unknown]

[unknown]

$δ$ -derivations of classical Lie superalgebras.

$κ$ -Minkowski spacetimes and DSR algebras: fresh look and old problems.

Абелевы расширения модулярных алгебр Ли

Абсолютные делители нуля в йордановых парах и алгебрах Ли

Автоморфизмы унипотентных подгрупп групп лиева типа малых рангов

Алгебра относительно-примитивных элементов.

Алгебраические группы, ассоциированные с картановскими p-алгебрами Ли

Currently displaying 1 – 20 of 276