Đoàn, Trung Cường
Published in
Journal of Algebra

We study Noetherian local rings whose all formal fibers are of dimension zero. Universal catenarity and going-up property of the canonical map to the completion are considered. We present several characterizations of these rings, including a characterization of Weierstrass preparation type. A characterization of local rings with going up property b...

Maksimau, Ruslan
Published in
Journal of Algebra

Stroppel and Webster have introduced a grading on the cyclotomic q-Schur algebra Sds. We prove that the obtained graded algebra is graded Morita equivalent to a Koszul algebra. The proof is based on a result of Rouquier, Shan, Varagnolo and Vasserot that identifies the category mod(Sds) with a subcategory of an affine parabolic category O of type A...

Rosso, Daniele
Published in
Journal of Algebra

The Iwahori–Hecke algebra of the symmetric group is the convolution algebra of GLn-invariant functions on the variety of pairs of complete flags over a finite field. Considering convolution on the space of triples of two flags and a vector we obtain the mirabolic Hecke algebra Rn, which had originally been described by Solomon. In this paper we giv...

Duong, Minh Thanh Ushirobira, Rosane
Published in
Journal of Algebra

In this paper, we generalize some results on quadratic Lie algebras to quadratic Lie superalgebras, by applying graded Lie algebras tools. We establish a one-to-one correspondence between non-Abelian quadratic Lie superalgebra structures and nonzero even super-antisymmetric 3-forms satisfying a structure equation. An invariant number of quadratic L...

Du, Jie Gu, Haixia
Published in
Journal of Algebra

We reconstruct the quantum enveloping superalgebra U(glm|n) over Q(υ) via (finite dimensional) quantum Schur superalgebras. In particular, we obtain a new basis containing the standard generators for U(glm|n) and explicit multiplication formulas of an arbitrary basis element by a generator.

Schaeffer Fry, Amanda A.
Published in
Journal of Algebra

The so-called “local–global” conjectures in the representation theory of finite groups relate the representation theory of G to that of certain proper subgroups, such as the normalizers of particular p-groups. Recent results by several authors reduce some of these conjectures to showing that a certain collection of stronger conditions holds for all...

Araújo, João Konieczny, Janusz Malheiro, António
Published in
Journal of Algebra

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the univer...

Kimura, Shunichi Kuroda, Shigeru Takahashi, Nobuyoshi
Published in
Journal of Algebra

For a multivariate power series f, let Cone(f) denote the cone generated by the exponents of the monomials with nonzero coefficients. Assume that f is an expansion of a rational function p/q with gcd(p,q)=1. Then we prove that the closure Cone¯(f) is equal to Cone(p)+Cone(q). As applications, we show the irrationality of Euler–Chow series of certai...

Liau, Pao-Kuei Liu, Cheng-Kai
Published in
Journal of Algebra

We prove that if a semisimple real or complex Banach algebra A possesses an algebraic derivation whose invariants are algebraic, then A is finite-dimensional. This result is a full generalization of a recent result by Haily, Kaidi and Palacios (2011) [15] for the case of inner derivations in complex semisimple Banach algebras. The analogous result ...

Caicedo, Mauricio del Río, Ángel
Published in
Journal of Algebra

Let G be a finite group, ZG the integral group ring of G and U(ZG) the group of units of ZG. The Congruence Subgroup Problem for U(ZG) is the problem of deciding if every subgroup of finite index of U(ZG) contains a congruence subgroup, i.e. the kernel of the natural homomorphism U(ZG)→U(ZG/mZG) for some positive integer m. The congruence kernel of...