-categoricity of products of 1-unary algebras
Philip Olin (1975)
Colloquium Mathematicae
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Philip Olin (1975)
Colloquium Mathematicae
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Jan Waszkiewicz (1973)
Colloquium Mathematicae
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A. Huckleberry, H. Sebert (2013)
Annales de l’institut Fourier
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Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities for eigensections approaching a semiclassical ray. Here is a normal compact toric variety and is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate...
Zenobia Anusiak (1971)
Colloquium Mathematicae
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Daniela La Mattina (2008)
Bollettino dell'Unione Matematica Italiana
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Let be a proper variety of associative algebras over a field of characteristic zero. It is well-known that can have polynomial or exponential growth and here we present some classification results of varieties of polynomial growth. In particular we classify all subvarieties of the varieties of almost polynomial growth, i.e., the subvarieties of and , where is the Grassmann algebra and is the algebra of upper triangular matrices.
Lior Bary-Soroker, Arno Fehm, Sebastian Petersen (2014)
Annales de l’institut Fourier
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A variety over a field is of Hilbert type if is not thin. We prove that if is a dominant morphism of -varieties and both and all fibers , , are of Hilbert type, then so is . We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Thélène and Sansuc on algebraic groups.
Igor Nikolaev (2015)
Czechoslovak Mathematical Journal
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The paper studies applications of -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension , and . In conclusion, we consider two numerical examples illustrating our main results.
Anders S. Buch, Pierre-Emmanuel Chaput, Leonardo C. Mihalcea, Nicolas Perrin (2013)
Annales scientifiques de l'École Normale Supérieure
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The product of two Schubert classes in the quantum -theory ring of a homogeneous space is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on . We show that if is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to that take the marked points to general Schubert varieties and...
Xinhong Chen, Ming Lu (2015)
Colloquium Mathematicae
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Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let and be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of . As a corollary, we find that if and only if if and only if .
Lidija Goračinova-Ilieva, Smile Markovski (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let be a positive integer. An algebra is said to have the property if all of its subalgebras generated by two distinct elements have exactly elements. A variety of algebras is a variety with the property if every member of has the property . Such varieties exist only in the case of prime power. By taking the universes of the subalgebras of any finite algebra of a variety with the property , , blocks of Steiner system of type are obtained. The stated correspondence...
Emmanuel Letellier (2013)
Journal of the European Mathematical Society
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Given a tuple of irreducible characters of we define a star-shaped quiver together with a dimension vector . Assume that is generic. Our first result is a formula which expresses the multiplicity of the trivial character in the tensor product as the trace of the action of some Weyl group on the intersection cohomology of some (non-affine) quiver varieties associated to . The existence of such a quiver variety is subject to some condition. Assuming that this condition is satisfied,...
Alexei N. Skorobogatov, Yuri G. Zahrin (2014)
Journal of the European Mathematical Society
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Let and be smooth and projective varieties over a field finitely generated over , and let and be the varieties over an algebraic closure of obtained from and , respectively, by extension of the ground field. We show that the Galois invariant subgroup of Br Br( has finite index in the Galois invariant subgroup of Br. This implies that the cokernel of the natural map Br Br Br is finite when is a number field. In this case we prove that the Brauer–Manin set of the...
Walter Rudin (1981)
Annales Polonici Mathematici
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Viktor Petrov, Nikita Semenov, Kirill Zainoulline (2008)
Annales scientifiques de l'École Normale Supérieure
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Let be a semisimple linear algebraic group of inner type over a field , and let be a projective homogeneous -variety such that splits over the function field of . We introduce the -invariant of which characterizes the motivic behavior of , and generalizes the -invariant defined by A. Vishik in the context of quadratic forms. We use this -invariant to provide motivic decompositions of all generically split projective homogeneous -varieties, e.g. Severi-Brauer varieties,...
Raymundo Bautista (2006)
Colloquium Mathematicae
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Let Λ be an artin algebra. We prove that for each sequence of non-negative integers there are only a finite number of isomorphism classes of indecomposables , the bounded derived category of Λ, with for all i ∈ ℤ and E(X) the endomorphism ring of X in if and only if , the bounded derived category of the category of all left Λ-modules, has no generic objects in the sense of [4].
Shiquan Ruan, Li Wang, Haicheng Zhang (2024)
Czechoslovak Mathematical Journal
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For any positive integer , let be a linearly oriented quiver of type with vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories and , where and are the two extriangulated categories corresponding to the representation category of and the morphism category of projective representations of , respectively. As a...
Aldo Victorio Figallo, Gustavo Pelaitay (2015)
Mathematica Bohemica
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In 2000, Figallo and Sanza introduced -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class of tense -valued Łukasiewicz-Moisil algebras (or tense LM-algebras), namely -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...
Marek Karaś (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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We present an example of finite mappings of algebraic varieties f:V → W, where V ⊂ kⁿ, , and such that and gdeg F = 1 < gdeg f (gdeg h means the number of points in the generic fiber of h). Thus, in some sense, the result of this note improves our result in J. Pure Appl. Algebra 148 (2000) where it was shown that this phenomenon can occur when V ⊂ kⁿ, with m ≥ n+2. In the case V,W ⊂ kⁿ a similar example does not exist.
Edoardo Ballico, Alessandra Bernardi (2013)
Annales Polonici Mathematici
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Let F be a homogeneous polynomial of degree d in m + 1 variables defined over an algebraically closed field of characteristic 0 and suppose that F belongs to the sth secant variety of the d-uple Veronese embedding of into but that its minimal decomposition as a sum of dth powers of linear forms requires more than s summands. We show that if s ≤ d then F can be uniquely written as , where are linear forms with t ≤ (d-1)/2, and Q is a binary form such that with ’s linear forms...
Yasuhiko Kamiyama (2003)
Fundamenta Mathematicae
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For G = SU(n), Sp(n) or Spin(n), let be the centralizer of a certain SU(2) in G. We have a natural map . For a generator α of , we describe J⁎(α). In particular, it is proved that is injective.