03688nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100008900240245012000329250001800449264007500467300004100542336002600583337002600609338003600635347002400671490006300695505058100758520123001339650001902569650002402588650003402612650001902646650002402665650001402689700008602703700008402789710003402873773002602907776003602933776003602969776003603005830006303041856004603104912001503150999001703165978-3-031-58148-9DE-He21320251030112043.0cr nn 008mamaa240515s2024    sz |    s    |||| 0|eng d  a97830315814899978-3-031-58148-97 a10.1007/978-3-031-58148-92doi 4aQA150-272 7aPBF2bicssc 7aMAT0020002bisacsh 7aPBF2thema1 aKurdachenko, Leonid.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97686410aGeneral Theory of Leibniz Algebrash[electronic resource] /cby Leonid Kurdachenko, Oleksandr Pypka, Igor Subbotin.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aX, 166 p. 1 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSynthesis Lectures on Mathematics & Statistics,x1938-17510 aElementary Properties and Connections -- Structure of Cyclic Leibniz Algebras -- Leibniz Algebras whose Proper Sub-algebras are Lie Algebras -- Leibniz Algebras whose Proper Sub-algebras are Ideals -- Leibniz Algebras in which the Relation “to be an ideal” is Transitive -- Leibniz Algebras whose Proper Sub-algebras are either Ideals or Contra-ideals -- Influence of Ideals and Self-idealizing Sub-algebras on the Structure of Leibniz Algebras -- Influence of Anti-commutativity on the Structure of Leibniz Algebras -- Analogue of Schur's Theorem and its Generalizations.  aThis book discusses many interesting results have been obtained in Leibniz algebras over the past two decades. The authors not only summarize recent results and methods successfully used in Leibniz algebras, but also show new prospective horizons. Any mathematical theories have a number of natural problems that arise in the process of its development, and these problems quite often have analogues in other areas such as differential geometry, homological algebra, classical algebraic topology, noncommutative geometry, etc. With this in mind the authors describe the general structure of Leibniz algebras that have already been discovered. This approach allows readers to see which parts of the theory should be developed further and also shows the significant differences of Leibniz algebras from Lie algebras. Recent results that constitute the naturally evolving general theory of the subject are then explored. In addition, this book: Summarizes results and methods used in Leibniz algebras and also shows new perspective horizons Discusses numerous interesting and promising results in the area of Leibniz algebras from the past two decades Addresses the significant differences of Leibniz algebras from Lie algebras. 0aAlgebra.91501 0aMathematics.965523 0aMathematical analysis.96417814aAlgebra.9150124aMathematics.96552324aAnalysis.1 aPypka, Oleksandr.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9768651 aSubbotin, Igor.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9768662 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303158147208iPrinted edition:z978303158149608iPrinted edition:z9783031581502 0aSynthesis Lectures on Mathematics & Statistics,x1938-175140uhttps://doi.org/10.1007/978-3-031-58148-9  aZDB-2-SXSC  c59876d59876