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Special biserial algebras with no outer derivations

Ibrahim Assem, Juan Carlos Bustamante, Patrick Le Meur (2011)

Colloquium Mathematicae

Let A be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of A with coefficients in the bimodule A vanishes if and only if A is representation-finite and simply connected (in the sense of Bongartz and Gabriel), if and only if the Euler characteristic of Q equals the number of indecomposable non-uniserial projective-injective A-modules (up to isomorphism). Moreover, if this is the case, then all the higher Hochschild cohomology groups...

Special modules for R ( PSL ( 2 , q ) )

Liufeng Cao, Huixiang Chen (2023)

Czechoslovak Mathematical Journal

Let R be a fusion ring and R ℂ : = R ⊗ ℤ ℂ be the corresponding fusion algebra. We first show that the algebra R ℂ has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, R ℂ admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly determine the special module of the interpolated fusion algebra R ( PSL ( 2 , q ) ) : = r ( PSL ( 2 , q ) ) ⊗ ℤ ℂ up to isomorphism, where r ( PSL ( 2 , q ) ) is the interpolated...

Spinors in braided geometry

Mićo Đurđević, Zbigniew Oziewicz (1996)

Banach Center Publications

Let V be a ℂ-space, σ ∈ E n d ( V ⊗ 2 ) be a pre-braid operator and let F ∈ l i n ( V ⊗ 2 , ℂ ) . This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra C l ( V , σ , 0 ) ≡ V ∧ ( σ ) . If σ ≠ σ - 1 and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...

Split-null extensions of strongly right bounded rings.

Gary F. Birkenmeier (1990)

Publicacions Matemàtiques

A ring is said to be strongly right bounded if every nonzero right ideal contains a nonzero ideal. In this paper strongly right bounded rings are characterized, conditions are determined which ensure that the split-null (or trivial) extension of a ring is strongly right bounded, and we characterize strongly right bounded right quasi-continuous split-null extensions of a left faithful ideal over a semiprime ring. This last result partially generalizes a result of C. Faith concerning split-null extensions...

Square subgroups of rank two abelian groups

A. M. Aghdam, A. Najafizadeh (2009)

Colloquium Mathematicae

Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.

Squared cycles in monomial relations algebras

Brian Jue (2006)

Open Mathematics

Let 𝕂 be an algebraically closed field. Consider a finite dimensional monomial relations algebra Λ = 𝕂 Γ 𝕂 Γ I I of finite global dimension, where Γ is a quiver and I an admissible ideal generated by a set of paths from the path algebra 𝕂 Γ . There are many modules over Λ which may be represented graphically by a tree with respect to a top element, of which the indecomposable projectives are the most natural example. These trees possess branches which correspond to right subpaths of cycles in the quiver. A pattern...

Stability of commuting maps and Lie maps

J. Alaminos, J. Extremera, Š. Špenko, A. R. Villena (2012)

Studia Mathematica

Let A be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on A is near an actual commuting continuous linear (resp. quadratic) map on A. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.

Currently displaying 2781 – 2800 of 3997