| 11. | Basic examples of almost commutative rings involve differential operators.
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| 12. | The commutators are second order differential operators from to.
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| 13. | Given the particular differential operators involved, this is a linear partial differential equation.
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| 14. | The exterior derivative commutes with natural differential operator.
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| 15. | A algebraic differential operators can also be defined.
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| 16. | :You can define the transpose as the formal adjoint of the differential operator.
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| 17. | This extension of the above differential operator need not be constrained only to real powers.
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| 18. | However, non-linear differential operators, such as the Schwarzian derivative also exist.
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| 19. | It can be identified with the Hopf algebra of graded differential operators at the origin.
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| 20. | The index of an elliptic differential operator obviously vanishes if the operator is self adjoint.
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