152,053 research outputs found
Koszul differential graded algebras and BGG correspondence
The concept of Koszul differential graded algebra (Koszul DG algebra) is
introduced. Koszul DG algebras exist extensively, and have nice properties
similar to the classic Koszul algebras. A DG version of the Koszul duality is
proved. When the Koszul DG algebra is AS-regular, the Ext-algebra of
is Frobenius. In this case, similar to the classical BGG correspondence,
there is an equivalence between the stable category of finitely generated left
-modules, and the quotient triangulated category of the full triangulated
subcategory of the derived category of right DG -modules consisting of all
compact DG modules modulo the full triangulated subcategory consisting of all
the right DG modules with finite dimensional cohomology. The classical BGG
correspondence can derived from the DG version.Comment: 29 page
Intense terahertz laser fields on a two-dimensional electron gas with Rashba spin-orbit coupling
The spin-dependent density of states and the density of spin polarization of
an InAs-based two-dimensional electron gas with the Rashba spin-orbit coupling
under an intense terahertz laser field are investigated by utilizing the
Floquet states to solve the time-dependent Schr\"odinger equation.
It is found that both densities are strongly affected by the terahertz laser
field. Especially a terahertz magnetic moment perpendicular to the external
terahertz laser field in the electron gas is induced. This effect can be used
to convert terahertz electric signals into terahertz magnetic ones efficiently.Comment: 3 pages, 3 figures, a typo in Fig. 3(b) is correcte
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