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Results 1 - 10
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2,607
Stable equivalence of knots on surfaces and . . .
, 2008
"... We introduce an equivalence relation, called stable equivalence, on knot diagrams and closed curves on surfaces. We give bijections between the set of abstract knots, the set of virtual knots, and the set of the stable equivalence classes of knot diagrams on surfaces. Using these bijections, we defi ..."
Abstract
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We introduce an equivalence relation, called stable equivalence, on knot diagrams and closed curves on surfaces. We give bijections between the set of abstract knots, the set of virtual knots, and the set of the stable equivalence classes of knot diagrams on surfaces. Using these bijections, we
Stable equivalences of adjoint type
- Forum Math
"... In this paper we define a class of stable equivalences, namely, the stable equivalences of adjoint type, and study the Hochschild cohomology groups of algebras that are linked by a stable equivalence of adjoint type. This notion of adjoint type is a special case of Morita type, covers the stable equ ..."
Abstract
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Cited by 7 (2 self)
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In this paper we define a class of stable equivalences, namely, the stable equivalences of adjoint type, and study the Hochschild cohomology groups of algebras that are linked by a stable equivalence of adjoint type. This notion of adjoint type is a special case of Morita type, covers the stable
Stable Equivalence And Generic Modules
"... . Let and \Gamma be finite dimensional algebras. It is shown that any stable equivalence f : mod ! mod \Gamma between the categories of finitely generated modules induces a bijection M 7! M f between the sets of isomorphism classes of generic modules over and \Gamma such that the endolength of M f ..."
Abstract
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Cited by 5 (0 self)
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. Let and \Gamma be finite dimensional algebras. It is shown that any stable equivalence f : mod ! mod \Gamma between the categories of finitely generated modules induces a bijection M 7! M f between the sets of isomorphism classes of generic modules over and \Gamma such that the endolength of M f
The stable equivalence and cancellation problems
- Comment. Math. Helv
, 2004
"... Abstract. Let K be an arbitrary field of characteristic 0, and A n the n-dimensional affine space over K. A well-known cancellation problem asks, given two algebraic varieties V1, V2 ⊆ A n with isomorphic cylinders V1 × A 1 and V2 × A 1, whether V1 and V2 themselves are isomorphic. In this paper, we ..."
Abstract
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Cited by 4 (2 self)
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, we focus on a related problem: given two varieties with equivalent (under an automorphism of A n+1) cylinders V1 × A 1 and V2 × A 1, are V1 and V2 equivalent under an automorphism of A n? We call this stable equivalence problem. We show that the answer is positive for any two curves V1, V2 ⊆ A 2
STABLE EQUIVALENCES RELATED WITH SYZYGY FUNCTORS
"... Abstract. Let
: mod mod be a stable equivalence between nite dimensional self-injective algebras over a eld. Then
preserves triangles in the triangulated category mod if and only if
commutes with syzygy functors. As an application, we study some stable equivalence induced by socle equivalen ..."
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Abstract. Let
: mod mod be a stable equivalence between nite dimensional self-injective algebras over a eld. Then
preserves triangles in the triangulated category mod if and only if
commutes with syzygy functors. As an application, we study some stable equivalence induced by socle
STABLE EQUIVALENCES OF GRADED ALGEBRAS
"... obtained by factoring out those maps that factor through a graded projective module. We say that Λ and Γ are graded stably equivalent if there is an equivalence α: gr Λ ≈ → gr ..."
Abstract
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Cited by 1 (1 self)
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obtained by factoring out those maps that factor through a graded projective module. We say that Λ and Γ are graded stably equivalent if there is an equivalence α: gr Λ ≈ → gr
Representation dimension: an invariant under stable equivalence
- TRANS. AMER. MATH. SOC
, 2004
"... In this paper, we prove that the representation dimension is an invariant under stable equivalence. ..."
Abstract
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Cited by 6 (0 self)
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In this paper, we prove that the representation dimension is an invariant under stable equivalence.
A NOTE ON THE STABLE EQUIVALENCE PROBLEM
"... Abstract. We provide counterexamples to the stable equivalence problem in every dimension d ≥ 2. That means that we construct hypersurfaces H1,H2 ⊂ C d+1 whose cylinders H1 ×C and H2 ×C are equivalent hypersurfaces in C d+2, although H1 and H2 themselves are not equivalent by an automorphism of C d+ ..."
Abstract
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Cited by 1 (1 self)
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Abstract. We provide counterexamples to the stable equivalence problem in every dimension d ≥ 2. That means that we construct hypersurfaces H1,H2 ⊂ C d+1 whose cylinders H1 ×C and H2 ×C are equivalent hypersurfaces in C d+2, although H1 and H2 themselves are not equivalent by an automorphism of C d
Results 1 - 10
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