.. _session_1B:
Online Training Session 1, Part B
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Defining groups and structure theory.
1. Questions from Part A
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Welcome back. Questions from previous hour. Function arguments/outputs queries: ``whattype "function" ?``, ``"function"@("input")``, inputs/outputs for the + function, e.g. ``+@(mat,int)``
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2. Data Types, Root Datum
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Data type: LieType, atlas functions: ``simply_connected``, ``adjoint``, ``simple_roots``, ``simple_coroots``. Root datum in atlas, isogenies; :math:`SL(2)`, :math:`GL(2)`, :math:`PSL(2)`
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3. More about Lie Groups
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More Lie groups, The file groups.at, realform data type, GL(2,R), Sp(4,R), ``posroots``, ``poscorrots``, ``rho``, ``GL(3,R)``, ``SL(3,R)``
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4. Fundamental Weight Coordinates, :math:`Sp(8,\mathbb{R})`
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The file lietypes.at, strings, type C4, fundamental weight coordinates, :math:`Sp(8,\mathbb{R})`
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5. Simple Roots of :math:`SL(5,\mathbb{R})`
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Simple roots of :math:`SL(5,\mathbb{R})`, atlas coordinates.
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6. More on Coordinates
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More on atlas' choice of coordinates, help files.
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7. The atlas-functions.help File
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The file atlas-functions.help
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8. Get Lie Groups Information
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More Lie group information, Lie algebra, connectednes, root datum, split, quasisplit, adjoint; ``nr_of_Cartan_classes``, ``print_cartan_info`` (for a real torus), imaginary, real and complex roots
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9. Real Forms
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``real_forms``, for loop to print real forms, cartan classes along realforms, sp(4)
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10. Inner Class
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real forms in an inner class. :math:`SL(5,\mathbb{R})`, distinguished involution, outer outomorphisms
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