1,721,300 research outputs found
A characterization of varieties of algebras of proper central exponent greater than two
Full text linkLet F be a field of characteristic zero and let V be a variety of associative F-algebras. In [19] Regev introduced a numerical sequence measuring the growth of the proper central polynomials of a generating algebra of V. Such sequence c delta n(V), n >= 1, is called the sequence of proper central polynomials of V and in [12], [13] the authors computed its exponential growth. This is an invariant of the variety. They also showed that c delta n(V) either grows exponentially or is polynomially bounded. The purpose of this paper is to characterize the varieties of associative algebras whose exponential growth of c delta n(V) is greater than two. As a consequence, we find a characterization of the varieties whose corresponding exponential growth is equal to two. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/)
*-Graded Capelli polynomials and their asymptotics
Full text linkLet F < YU Z, *> be the free *-superalgebra over a field F of characteristic zero and let Gamma(M +/-, L +/-)* be the T-Z2* - ideal generated by the set. of the s-graded Capelli polynomi- als Cap(M+)((Z2,)*())[Y+, X], Cap(L+)((Z2,)*())[Z(+), X], Cap(L-)((Z2,)*())[Z-,X] alternating on M +/- symmetric variables of homogeneous degree zero, on M- skew variables of homogeneous degree zero, on L+ symmetric variables of homogeneous degree one and on L- skew variables of homogeneous degree one, respectively. We study the asymptotic behavior of the sequence of *-graded codimensions of Gamma(M)(+/-,L)(+/-)*. In particular, we prove that the s-graded codimensions of the finite dimensional simple *-superalgebras are asymptotically equal to the *-graded codimensions of Gamma(M)(+/-,L)(+/-)*, for some fixed natural numbers M+, M-, L+ and L-
Leveraging Relational Information for Learning Weakly Disentangled Representations
No full textDisentanglement is a difficult property to enforce in neural representations. This might be due, in part, to a formalization of the disentanglement problem that focuses too heavily on separating relevant factors of variation of the data in single isolated dimensions of the neural representation. We argue that such a definition might be too restrictive and not necessarily beneficial in terms of downstream tasks. In this work, we present an alternative view over learning (weakly) disentangled representations, which leverages concepts from relational learning. We identify the regions of the latent space that correspond to specific instances of generative factors, and we learn the relationships among these regions in order to perform controlled changes to the latent codes. We also introduce a compound generative model that implements such a weak disentanglement approach. Our experiments shows that the learned representations can separate the relevant factors of variation in the data, while preserving the information needed for effectively generating high quality data samples
Varieties with at most cubic growth
Full text linkLet V be a variety of non necessarily associative algebras over a field of characteristic zero. The growth of V is determined by the asymptotic behavior of the sequence of codimensions c(n) (V),n = 1,2,..., and here we study varieties of polynomial growth. We classify all possible growth of varieties V of algebras satisfying the identity x(yz) equivalent to 0 such that c(n) (V) < C-n(alpha) with 1 <= alpha < 3, for some constant C. We prove that if 1 <= alpha < 2 then c(n) (V) <= C-1n, and if 2 <= alpha < 3, then c(n)(V) <= C(2)n(2), for some constants C-1, C-2
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Correspondence between some metabelian varieties and left nilpotent varieties
No full textIn the class of left nilpotent algebras of index two it was proved that there are no varieties of fractional polynomial growth ≈nα with 1<2 and 2<3 instead it was established the existence of a variety of fractional polynomial growth with [Formula presented]. In this paper we investigate similar problems for varieties of commutative or anticommutative metabelian algebras. We construct a correspondence between left nilpotent algebras of index two and commutative metabelian algebras or anticommutative metabelian algebras and we prove that the codimensions sequences of the corresponding algebras coincide up to a constant. This allows us to transfer the above results concerning varieties of left nilpotent algebras of index two to varieties of commutative or anticommutative metabelian algebras
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