A retrospect of the research in nonassociative algebras in IME-USP

DOI10.1007/s40863-021-00248-xzbMath1502.17001OpenAlexW3185528010WikidataQ121627484 ScholiaQ121627484MaRDI QIDQ2082030

Luiz Antonio Peresi, Ivan Pavlovic Shestakov, Lucia S. I. Murakami

Publication date: 30 September 2022

Published in: São Paulo Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40863-021-00248-x

zbMATH Keywords

loopssuperalgebrasnonassociative algebras

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02) History of nonassociative rings and algebras (17-03)

Cites Work

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• Representation type of Jordan algebras
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• Constants of partial derivations and primitive operations
• Superalgebras and counterexamples
• Invariants of \(\mathrm G_2\) and Spin(7) in positive characteristic
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• Examples of self-iterating Lie algebras
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• An application of lattice basis reduction to polynomial identities for algebraic structures
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• Graphs and nonassociative algebras
• Every Akivis algebra is linear
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• Shape identities in genetic algebras
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• On identities of baric algebras and superalgebras
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• The radical in alternative baric algebras
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• Simple finite-dimensional modular noncommutative Jordan superalgebras
• Gradings on simple Jordan and Lie algebras
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• Solutions of the Bernstein problem in the nonregular case
• Loop of formal diffeomorphisms and Faà di Bruno coloop bialgebra
• On the free Jordan algebras
• Right alternative bimodules over Cayley algebra and coordinatization theorem
• The Freiheitssatz for generic Poisson algebras
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• On filtered multiplicative bases of some associative algebras.
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• A characterization of Lie algebras of skew-symmetric elements
• Geometric classification of nilpotent Jordan algebras of dimension five
• Finite-dimensional right alternative superalgebras with semisimple strongly alternative even part
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• Irreducible bimodules over alternative algebras and superalgebras
• On Right Alternative Superalgebras
• The variety of three-dimensional real Jordan algebras
• Abelian-by-Cyclic Moufang Loops
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• Kimmerle conjecture for the Held and O'Nan sporadic simple groups
• The Bar-Radical of a Class of Almost Alternative Baric Algebras
• The Chevalley and Costant theorems for Mal’tsev algebras
• Noetherianness of wreath products of Abelian Lie algebras with respect to equations of universal enveloping algebra
• Nuclear Elements of Degree 6 in the Free Alternative Algebra
• Jordan bimodules over the superalgebras 𝑃(𝑛) and 𝑄(𝑛)
• An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
• On a construction of self-dual gauge fields in seven dimensions
• Polynomial Identities for Bernstein Algebras of Simple Mendelian Inheritance
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• Genetic Algebras Satisfying Bernstein's Stationarity Principle
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• Moufang loops and alternative algebras
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• FREE MALCEV SUPERALGEBRA ON ONE ODD GENERATOR
• On idempotents and isomorphisms of multiplication algebras of bernstein algebras
• Counterexamples to the Specht problem
• Free generic Poisson fields and algebras
• A non-associative Baker-Campbell-Hausdorff formula
• Derivations of the Lie algebra of infinite strictly upper triangular matrices over a commutative ring
• Description of costandard modules for Schur superalgebra S(2|2) in positive characteristic
• A finite presentation of Jordan algebras
• Rings of constants of linear derivations on Fermat rings
• Nilpotent Steiner loops of class 2
• COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p³
• REPRESENTATIONS OF EXCEPTIONAL SIMPLE JORDAN SUPERALGEBRAS OF CHARACTERISTIC 3^#
• Some graded identities of the Cayley–Dickson algebra
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• Central Quotients and Coverings of Steinberg Unitary Lie Algebras
• The free commutative automorphic $2$-generated loop of nilpotency class $3$
• Higher identities for the ternary commutator
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• Hopf algebras in non-associative Lie theory
• The Wedderburn b-decomposition for a class of almost alternative baric algebras
• The Nucleus of the Free Alternative Algebra
• Lagrange's theorem for Moufang loops
• THE FREE ALTERNATIVE SUPERALGEBRA ON ONE ODD GENERATOR
• PBW-Pairs of Varieties of Linear Algebras
• Simple Classical Lie Algebras in Characteristic 2 and Their Gradations, II
• ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS
• Classification of Trilinear Operations
• The Nagata automorphism is wild
• The Universal Multiplicative Envelope of the Free Malcev Superalgebra on One Odd Generator
• GROUPS WITH TRIALITY
• Free Steiner triple systems and their automorphism groups
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• On Commuting U-Operators in Jordan Algebras
• Multiplication formulas in Moufang loops
• Jordan Superalgebras of Type and the Wedderburn Principal Theorem (WPT)
• Structurable superalgebras of Cartan type
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• Speciality of Lie-Jordan algebras
• Irreducible unital right alternative bimodules
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