531.3 531.3 413.2 413.2 295.1 531.3 531.3 649.3 531.3 295.1 885.4 795.8 885.4 443.6 /Differences[33/exclam/quotedblright/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 0 708.3 1041.7 972.2 736.1 833.3 812.5 902.8 972.2 902.8 972.2 0 0 902.8 729.2 659.7 /FirstChar 33 833.3 805.6 819.4 798.6 888.9 777.8 743.1 833.3 812.5 319.4 576.4 840.3 708.3 1020.8 /F2 13 0 R 277.8 972.2 625 625 625 625 416.7 479.2 451.4 625 555.6 833.3 555.6 555.6 538.2 625 When I was a student, I majored in physics and maths. << /Name/F2 /Type/Font endobj endobj /Widths[392.4 687.5 1145.8 687.5 1183.3 1027.8 381.9 534.7 534.7 687.5 1069.5 381.9 /Subtype/Type1 32 0 obj A Hopf Algebra is endowed with certain structures which have very physical counterparts. endobj << �����*���zҙ?�ze����.tΨ��4��E?t�^ɱ�B��>HF���hx�&DJ�m\q�P���K[�6� The same approach works when solving physics problems (most of the time). >> /Type/Font /Widths[660.7 490.6 632.1 882.1 544.1 388.9 692.4 1062.5 1062.5 1062.5 1062.5 295.1 /Type/Font 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 endstream /Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5
343.8 593.8 312.5 937.5 625 562.5 625 593.8 459.5 443.8 437.5 625 593.8 812.5 593.8 The most familiar division algebras are R, C and H (i.e. 28 0 obj /LastChar 196 /FirstChar 33 stream 277.8 972.2 625 625 625 625 416.7 479.2 451.4 625 555.6 833.3 555.6 555.6 538.2 625 How to manipulate basic equations to solve for any variable. On the other hand, what if you had to solve the same problem for the time, The lesson in this example is that you can extract all three variables — distance, acceleration, and time — from the original equation. stream Take the following equation, for example, which relates the distance something has traveled (Now suppose that the physics problem asks you for the acceleration, not the distance. /Encoding 7 0 R �F �8*���ND�o� �Ms�J��c��{P�ۊZ�I?�E�A���R�w����(�.G������M��˕�6�����D�.#���Q��dD��{���&���`�eQJ��ǹ��g��(��.N��L�"LL����nG������^37a��]��M�͂ʖD��~���JD�|$G��Y>�2=
$\��r�S��3����r�xJ[u�?��m��n���f�>���-�>��$�������6�"]L�e~\M�YC�p����\�G�7�a7� �0�1'`�:��l1 �N1�$UC|6��lbS+�V'1ܲ�I�Ҹ�S��_큵�H6g}���e�����q�R��N*Wp�4�_!���m�- ����Sj��vEi� ߀�W6� /BaseFont/UWCPZJ+LCMSS8 endobj 708.3 708.3 826.4 826.4 472.2 472.2 472.2 649.3 826.4 826.4 826.4 826.4 0 0 0 0 0 659.7 1006.9 1006.9 277.8 312.5 625 625 625 625 625 805.6 555.6 590.3 902.8 972.2 1250 625 625 625 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 << There are so many examples to illustrate how important and useful abstract algebra is. Physics is built on top of maths and requires a good understanding of it. /Length 627 /Length 1285 /Encoding 7 0 R 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 1062.5 1062.5 826.4 826.4 173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis 10 0 obj If you're seeing this message, it means we're having trouble loading external resources on our website. xڝT[O�0~߯�#a�K�8{Z�t�4}�4��&n�H�,I�د�� mA����|��������3����qwP����F{�z�����o�8�f9�/�TT�ʼx���{�NH�4�V+�Hd�;�M�M]�����wE���_�������"�j}�Pϩ��".9M"J�Ik�%R� /ProcSet[/PDF/Text/ImageC] ��x2�D8�41�������L����eLG�J�H�ܲ0�p�jc��YG����ͽ�8^��ٔ�sŎ�ja[P !rF�f1��4ϟ�v
8��_�ںnT�ો�$x���8� the algebra of the quaternions, spanned by the identity and the three Pauli matrices). 6 0 obj Take the following equation, for example, which relates the distance something has traveled ( s ) to its acceleration and the time it has been accelerated: /FirstChar 33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 826.4 295.1 826.4 531.3 826.4
812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] Introduction: what is a division algebra? 531.3 826.4 826.4 826.4 826.4 0 0 826.4 826.4 826.4 1062.5 531.3 531.3 826.4 826.4 /LastChar 196 Group theory, group representations, co-representations, braid groups, Lie algebra, etc. /Widths[354.2 625 1041.7 625 1041.7 937.5 347.2 486.1 486.1 625 972.2 347.2 416.7 783.4 872.8 823.4 619.8 708.3 654.8 0 0 816.7 682.4 596.2 547.3 470.1 429.5 467 533.2 endobj /FontDescriptor 9 0 R endobj 1062.5 826.4] They all admit the unit element and an anti-involution (the conjugation) s.t.
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