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Homology and modular classes of Lie algebroids

Janusz Grabowski, Giuseppe Marmo, Peter W. Michor (2006)

Annales de l’institut Fourier

For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.

Homotopy theory of Hopf Galois extensions

Christian Kassel, Hans-Jürgen Schneider (2005)

Annales de l'institut Fourier

We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H -Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum group.

How to categorify one-half of quantum 𝔤𝔩(1|2)

Mikhail Khovanov (2014)

Banach Center Publications

We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra 𝔤𝔩(1|2).

Hyperkomplexní čísla a maticové algebry

Jindřich Bečvář, Vlastimil Dlab (2024)

Pokroky matematiky, fyziky a astronomie

V článku jsou ukázány tři procesy, kterými z tělesa reálných čísel vznikají algebry komplexních, dvojných, resp. duálních čísel, což jsou jediné neizomorfní algebry dimenze 2, které mají jednotkový prvek. Stejnými procesy vznikají z tělesa komplexních čísel algebry kvaternionů, antikvaternionů, resp. semikvaternionů, a stejnými procesy vznikají z kvaternionů algebry oktáv, antioktáv, resp. semioktáv. Následně je pozornost věnována reprezentacím komplexních, dvojných a duálních čísel, kvaternionů,...

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