. In the proof, change all occurrences of B before the displayed formula to I . After this formula, F → B should be defined by mapping every generator π i of F to the corresponding generator b i of B.

Share ". In the proof, change all occurrences of B before the displayed formula to I . After this formula, F → B should be defined by mapping every generator π i of F to the corresponding generator b i of B."

(1)

Errata to the appendix

There is a non-constructive step in the proof of Lemma A.2. This page indicates briefly how the problem is solved. There is also a correcting note with detailed proofs available at http://www.math.su.se/ ^∼ jesper/research/thesis/.

In Lemma A.2, add the assumption that B is discretely generated by a set I, which means that I is discrete and can index a set of generators of B. Change the power to A ^A

. In the proof, change all occurrences of B before the displayed formula to I . After this formula, F → B should be defined by mapping every generator π ⁱ of F to the corresponding generator b i of B.

In Corollary A.3, add as a fifth condition that an algebra is in C if its finitely generated subalgebras are. Begin the proof by noting that it is sufficient to consider finitely generated subalgebras of A, so that one may, without loss of generality, assume that A is generated by n generators. Replace the power by G ^G

ⁿ

.

In Theorem A.13, add the condition that C be closed under inductive limits.

Begin the proof by observing that every algebra is the inductive limit of its finitely generated subalgebras, so that it suffices to consider such algebras.

In the summary at the end, remove the claim that the original proof is constructive, because it has the same problem – the recursive counterexample given in the correcting note can be used to show this as well.

. In the proof, change all occurrences of B before the displayed formula to I . After this formula, F → B should be defined by mapping every generator π i of F to the corresponding generator b i of B.

Errata to the appendix

There is a non-constructive step in the proof of Lemma A.2. This page indicates briefly how the problem is solved. There is also a correcting note with detailed proofs available at http://www.math.su.se/ ^∼ jesper/research/thesis/.

In Lemma A.2, add the assumption that B is discretely generated by a set I, which means that I is discrete and can index a set of generators of B. Change the power to A ^A

. In the proof, change all occurrences of B before the displayed formula to I . After this formula, F → B should be defined by mapping every generator π ⁱ of F to the corresponding generator b i of B.

.

In Theorem A.13, add the condition that C be closed under inductive limits.

Begin the proof by observing that every algebra is the inductive limit of its finitely generated subalgebras, so that it suffices to consider such algebras.

In the summary at the end, remove the claim that the original proof is constructive, because it has the same problem – the recursive counterexample given in the correcting note can be used to show this as well.

Stockholm, May 26, 2005

Jesper Carlstr¨ om

. In the proof, change all occurrences of B before the displayed formula to I . After this formula, F → B should be defined by mapping every generator π i of F to the corresponding generator b i of B.

Errata to the appendix

There is a non-constructive step in the proof of Lemma A.2. This page indicates briefly how the problem is solved. There is also a correcting note with detailed proofs available at http://www.math.su.se/ ∼ jesper/research/thesis/.

In Lemma A.2, add the assumption that B is discretely generated by a set I, which means that I is discrete and can index a set of generators of B. Change the power to A A

. In the proof, change all occurrences of B before the displayed formula to I . After this formula, F → B should be defined by mapping every generator π i of F to the corresponding generator b i of B.

.

In Theorem A.13, add the condition that C be closed under inductive limits.

Begin the proof by observing that every algebra is the inductive limit of its finitely generated subalgebras, so that it suffices to consider such algebras.

In the summary at the end, remove the claim that the original proof is constructive, because it has the same problem – the recursive counterexample given in the correcting note can be used to show this as well.

Stockholm, May 26, 2005

Jesper Carlstr¨ om

There is a non-constructive step in the proof of Lemma A.2. This page indicates briefly how the problem is solved. There is also a correcting note with detailed proofs available at http://www.math.su.se/ ^∼ jesper/research/thesis/.

In Lemma A.2, add the assumption that B is discretely generated by a set I, which means that I is discrete and can index a set of generators of B. Change the power to A ^A

. In the proof, change all occurrences of B before the displayed formula to I . After this formula, F → B should be defined by mapping every generator π ⁱ of F to the corresponding generator b i of B.