A note on V-rings
A partition formula for Fibonacci numbers.
A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko’s theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.
A Priddy-type Koszulness criterion for non-locally finite algebras
A celebrated result by S. Priddy states the Koszulness of any locally finite homogeneous PBW-algebra, i.e. a homogeneous graded algebra having a Poincaré-Birkhoff-Witt basis. We find sufficient conditions for a non-locally finite homogeneous PBW-algebra to be Koszul, which allows us to completely determine the cohomology of the universal Steenrod algebra at any prime.
A properly infinite Banach *-algebra with a non-zero, bounded trace
A properly infinite C*-algebra has no non-zero traces. We construct properly infinite Banach *-algebras with non-zero, bounded traces, and show that there are even such algebras which are fairly "close" to the class of C*-algebras, in the sense that they can be hermitian or *-semisimple.
A property for locally convex *-algebras related to property (T) and character amenability
For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that has property (FH) if and only if G has property (T). On...
A property of the degree filtration of polynomial functors.
À propos des théories de Galois finies et infinies
À propos d'un théorème de Frobenius
A question on the discriminants of involutions of central division algebras.
A radical between Jacobson and Brown-McCoy radicals
A radical for right near-rings: the right Jacobson radical of type-0.
A reduction theorem for ring varieties whose subvariety lattice is distributive
We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.
A Reduction Theorem for the Primitivity of Tensor Products.
A remark about the Connes fusion tensor product.
A remark concerning commutativity modulo radical in Banach algebras
A remark on decomposable modules.
A remark on differential operator algebras and an equivalence of categories
A remark on growth relation.
A remark on -torsion-free modules