English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

From the four normed division algebras--the real numbers, complex numbers,quaternions and octonions, of dimension k=1, 2, 4 and 8, respectively--asystematic procedure gives a 3-cocycle on the Poincare superalgebra indimensions k+2=3, 4, 6 and 10, and a 4-cocycle on the Poincare superalgebra indimensions k+3=4, 5, 7 and 11. The existence of these cocycles follow fromspinor identities that hold only in these dimensions, and which are closelyrelated to the existence of the superstring in dimensions k+2, and thesuper-2-brane in dimensions k+3.  In general, an (n+1)-cocycle on a Lie superalgebra yields a `Lien-superalgebra': that is, roughly, an n-term chain complex equipped with abracket satisfying the axioms of a Lie superalgebra up to chain homotopy. Wethus obtain Lie 2-superalgebras extending the Poincare superalgebra indimensions k+2, and Lie 3-superalgebras extending the Poincare superalgebra indimensions k+3. We present evidence, based on the work of Sati, Schreiber andStasheff, that these Lie n-superalgebras describe infinitesimal `highersymmetries' of the superstring and 2-brane.  Generically, integrating a Lie n-superalgebra to a Lie n-supergroup yields a`Lie n-supergroup' that is hugely infinite-dimensional. However, when the Lien-superalgebra is obtained from an (n+1)-cocycle on a nilpotent Liesuperalgebra, there is a geometric procedure to integrate the cocycle to one onthe corresponding nilpotent Lie supergroup.  In general, a smooth (n+1)-cocycle on a supergroup yields a `Lien-supergroup': that is, a weak n-group internal to supermanifolds. Using ourgeometric procedure to integrate the 3-cocycle in dimensions k+2, we obtain aLie 2-supergroup extending the Poincare supergroup in those dimensions, andsimilarly integrating the 4-cocycle in dimensions k+3, we obtain a Lie3-supergroup extending the Poincare supergroup in those dimensions.

Division Algebras, Supersymmetry and Higher Gauge Theory