Cohomology Algebras of a Family of DG Skew Polynomial Algebras by Xuefeng Mao, Gui Ren

“…We find some examples, which indicate that the cohomology graded algebras of such kind of DG algebras may be not left (right) Gorenstein.…”
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Casimir operators, abelian subspaces and u-cohomology by Pierluigi Möseneder Frajria, Paolo Papi

“…We survey old and recent results by Kostant et al. on Casimir operators and abelian subspaces in Z_2-graded algebras. Our approach stresses and exploits the connection with u-cohomology.…”
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On the Cancellation Rule in the Homogenization by Victor Ufnarovski

“…We consider the possible ways of the homogenization of non-graded non-commutative algebra and show that it should be combined with the cancellation rule to get the mathematically adequate correspondence between graded and non-graded algebras.…”
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Defining relations of quantum symmetric pair coideal subalgebras by Stefan Kolb, Milen Yakimov

“…Our methods are based on star products on noncommutative ${\mathbb N}$-graded algebras. The resulting defining relations are expressed in terms of continuous q-Hermite polynomials and a new family of deformed Chebyshev polynomials.…”
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Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications by Naruhiko Aizawa

“…This elucidates physical relevance of the $\mathbb{Z}_2^n$-graded algebras. As an example of physically interesting algebra, we take $\mathbb{Z}_2^2$-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). …”
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Yangians and Yang–Baxter R-operators for ortho-symplectic superalgebras by J. Fuksa, A.P. Isaev, D. Karakhanyan, R. Kirschner

“…We start with the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the ortho-symplectic supergroup. …”
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Graded Medial <i>n</i>-Ary Algebras and Polyadic Tensor Categories by Steven Duplij

“…Toyoda’s theorem which connects (universal) medial algebras with abelian algebras is proven for the almost medial graded algebras introduced here. In a similar way we generalize tensor categories and braided tensor categories. …”
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CATEGORICAL COMPLEXITY by SAUGATA BASU, UMUT ISIK

“…We discuss several examples of this new definition in categories of wide common interest such as finite sets, Boolean functions, topological spaces, vector spaces, semilinear and semialgebraic sets, graded algebras, affine and projective varieties and schemes, and modules over polynomial rings. …”
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Expectancy-Value Beliefs of Early-Adolescent Hispanic and Non-Hispanic Youth by Nayssan Safavian, AnneMarie Conley

“…Expectancy for success and task value uniquely predicted seventh-grade achievement and eighth-grade algebra enrollment after controlling for prior achievement and a full set of demographic controls, including low socioeconomic status and English fluency. …”
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New examples of four dimensional AS-regular algebras by Caines, Ian

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Some interactions between Hopf Galois extensions and noncommutative rings by Armando Reyes, Fabio Calderón

“…In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew polynomial rings, PBW extensions and skew PBW extensions, etc.) …”
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Tensor Products and Crossed Differential Graded Lie Algebras in the Category of Crossed Complexes by Elif Iğde, Koray Yılmaz

“…In this paper, we present analogous definitions for Lie algebras within the framework of whiskered structures, bimorphisms, crossed complexes, crossed differential graded algebras, and tensor products. These definitions, given for groupoids in existing literature, have been adapted to establish a direct correspondence between these algebraic structures and Lie algebras. …”
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Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system by Zengo Tsuboi

“…It is known that there is a correspondence between representations of superalgebras and ordinary (non-graded) algebras. Keeping in mind this type of correspondence between the twisted quantum affine superalgebra Uq(gl(2r|1)(2)) and the non-twisted quantum affine algebra Uq(so(2r+1)(1)), we proposed, in the previous paper [1], a Wronskian solution of the T-system for Uq(so(2r+1)(1)) as a reduction (folding) of the Wronskian solution for the non-twisted quantum affine superalgebra Uq(gl(2r|1)(1)). …”
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High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative “Get It Quick and Get It Right” by Teresa K. Dunleavy

“…In so doing, I present a set of counterstories from three students in one ninth-grade Algebra 1 classroom. These students described transformative experiences in their perceptions of mathematical smartness. …”
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Universal Algebra I policy, access, and inequality: Findings from a national survey by Janine T. Remillard, John Y. Baker, Michael D. Steele, Nina D. Hoe, Anne Traynor

“…Only 26% of districts reported having universal enrollment policies; in these districts, linear regression indicated that an association with higher eighth grade Algebra I enrollment was moderated by poverty level (measured by FRL). …”
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Elementary states, supergeometry and twistor theory by Pilato, A, Pilato, Alejandro

“…</p> <p>A supermanifold is a ringed space consisting of an underlying classical manifold and an augmented sheaf of <strong>Z</strong>₂-graded algebras locally isomorphic to an exterior algebra. …”