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An antisymmetrizer, which projects out all symmetric tensors from tensor algebra. The canonical ✞ ✞ ✄ ✡q✼ ➜ . g. Hecke algebras, one obtains deformed Graßmann alge✆ bras ✑ . The presentation of the symmetric algebra reads ✧ Ð ♠ ➁ ✩ ✕ ❡ ✕ ❢ ✕ ❤ ✸ ✸ ✸ ❛ → ✤ ✩ ✏ ✖ ✞ ❢ ✕✘❡➆✞✎✕❣❢➆✞✖✕❣❤ ❤ ♦ → → → ✩ → → → ❡ ⑨ ❡ ⑨ ❡ ⑨ → → ✩ → → if ♥ → ❡ ❧❍→ ♥❏❨ ❡ ⑨ ⑨ ❡ ⑨ ✙ ✲ (2-39) 26 A Treatise on Quantum Clifford Algebras ✖ ✏ contains ❻✷❧ generators, → ❡ . This is a restriction of the Artin braid group, resp. its group ✕ ❡ .

These are different linear forms and their appearance is important in quantum physics. Moreover, we ✂✁☎✄✝✆✟✞✝✠☛✡ ✂✁☎✄✝✆✟✞✌☞✍✡ and are isomorphic as ✩ ❛ -graded algebras, but they possess different saw that canonical linear structures. The isomorphy, mediated by the Wick theorem, is nothing but a change in the product from the ✞ wedge to the dotted wedge and vice versa. Of course, one could ✄ introduce a new unit map ❹ or ✄ ❸ to avoid these problems, however, we will see that there are other obstructions which prevent this.

It was Woronowicz [136, 137] who studied systematically the theory of deformed Graßmann algebras. t. an antisymmetrizer, which projects out all symmetric tensors from tensor algebra. The canonical ✞ ✞ ✄ ✡q✼ ➜ . g. Hecke algebras, one obtains deformed Graßmann alge✆ bras ✑ . The presentation of the symmetric algebra reads ✧ Ð ♠ ➁ ✩ ✕ ❡ ✕ ❢ ✕ ❤ ✸ ✸ ✸ ❛ → ✤ ✩ ✏ ✖ ✞ ❢ ✕✘❡➆✞✎✕❣❢➆✞✖✕❣❤ ❤ ♦ → → → ✩ → → → ❡ ⑨ ❡ ⑨ ❡ ⑨ → → ✩ → → if ♥ → ❡ ❧❍→ ♥❏❨ ❡ ⑨ ⑨ ❡ ⑨ ✙ ✲ (2-39) 26 A Treatise on Quantum Clifford Algebras ✖ ✏ contains ❻✷❧ generators, → ❡ .

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A treatise on quantum Clifford algebras by Fauser.


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