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Lie groups

In: Mathematics for Physics An Illustrated Handbook

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  • Adam Marsh

Abstract

The following sections are included:Combining algebra and geometrySpaces with multiplication of pointsVector spaces with topologyLie groups and Lie algebrasThe Lie algebra of a Lie groupThe Lie groups of a Lie algebraRelationships between Lie groups and Lie algebrasThe universal cover of a Lie groupMatrix groupsLie algebras of matrix groupsLinear algebraMatrix groups with real entriesOther matrix groupsManifold properties of matrix groupsMatrix group terminology in physicsRepresentationsGroup actionsGroup and algebra representationsLie group and Lie algebra representationsCombining and decomposing representationsOther representationsClassification of Lie groupsCompact Lie groupsSimple Lie algebrasClassifying representations

Suggested Citation

  • Adam Marsh, 2018. "Lie groups," World Scientific Book Chapters, in: Mathematics for Physics An Illustrated Handbook, chapter 7, pages 111-140, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789813233928_0007
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    Keywords

    Portfolio Investment; Political Risk; Financial Risk; Equity Return; Market Efficiency; Stochastic Dominance; Risk Management; Derivatives; Foreign Currency Debt;
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    JEL classification:

    • F30 - International Economics - - International Finance - - - General

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