The $\imath$Serre relations and the corresponding Serre-Lusztig are formulated established for arbitrary $\imath$quantum groups arising from quantum symmetric pairs of Kac-Moody type.

Let R be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented R-modules that are closed under extensions. We also classify abelian subcategories of arbitrary R-modules that are closed under extensions and coproducts, when R is commutative and Noetherian. The method relies on comparison with ...

Given any additive category C with split idempotents, pseudokernels and pseudocokernels, we show that a subcategory B is coreflective if, only it precovering, closed under direct summands each morphism in has pseudocokernel belongs to B. We apply this result its dual to, among others, preabelian pretriangulated categories. As consequence, of it, precovering taking cokernels. On the other hand, ...

Combining work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and Texier and Zumbrun, we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite-cross-section duct the violation of the refined planar stability condition of Zumbrun–Serre, a viscous correction of the inviscid planar stability condition of Majda. More precisely, we ...

It was shown that the spin chain model coming from AdS/CFT correspondence satisfies the Yangian symmetry if we assume evaluation representation, though so far there is no explicit proof that the evaluation representation satisfies the Serre relation, which is one of the defining equations of the Yangian algebra imposing constraints on the whole algebraic structure. We prove completely that the ...