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Oct 28, 2020 at 8:29 comment added Sebastian Your involution lifts to an action $Dt\colon TM\to TM$. Then, you get a commuting diagram of the Clifford multiplication before and after the action of $t$ on both bundles.
Oct 28, 2020 at 8:10 comment added Kafka91 thank you for your answer! One question though: what do you mean when you say that the action is compatible with the Clifford-multiplication? Does it commute? Is it rather to be understood as a sort of homomorphism?
Oct 23, 2020 at 17:36 history answered Sebastian CC BY-SA 4.0